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By Carlos Calvo MEXICO CITY, April 28 (Reuters) - Mexico head for their 15th World Cup looking to break the second round barrier on foreign soil for the first time although their poor qualifying campaign suggests the odds are heavily stacked against them. The only times Mexico have reached the quarter-finals was when they hosted the finals in 1970 and 1986, the latter a 24-team tournament in which they were unbeaten in five matches, going out to Germany on penalties. Coach Miguel Herrera, however, will travel to Brazil believing his team can spring a shock by reaching at least the quarter-finals and possibly even go further. "If you don't start each tournament thinking of being champions then you don't have ambition," Herrera told Reuters in an interview. "We know it's hard -- history or what has happened to my predecessors who haven't even reached the fifth match -- can back up my words." It is surprising that Mexico has failed to live up to expectations at the World Cup given the soccer-crazy country of 100 million has one of the richest domestic leagues in the world. The national team, however, have failed to reach the last eight in the last five tournaments they have competed in since missing out altogether at Italia'90, the last time they failed to compete. Their path to Brazil was one of the poorest of their rich history as they failed to take advantage of the seething cauldron of their Azteca stadium and lost three coaches in a six-week period. FRAUGHT PATH Mexico finished fourth in the CONCACAF (Confederation of North and Central America and the Caribbean) qualifying final round, behind automatic qualifiers the United States, Costa Rica and Honduras, earning a place in the intercontinental playoff with New Zealand - and only after the U.S. had recorded a last gasp win over Panama on the final match day. Herrera was handed control for the two-legged playoff against the Oceania champions, who they crushed 9-3 on aggregate to grab one of the last tickets the finals. Their fraught path to the finals is hardly a good omen for success in Brazil, though Herrera, who was appointed to take the team through to the finals, remains upbeat. "The national team are in debt to their fans, every day we try to get results to reduce that debt and it will be paid off at the World Cup," the confident Herrera said. "The minimum demand the (Mexican) federation is making is to reach the famous fifth match but I say that if we reach the quarter-finals why not think we can go further." Mexico, however, are in the tough Group A in which they open against Cameroon on June 13 in Natal, then clash with hosts and favourites Brazil in Fortaleza four days later before facing Croatia in Recife on June 23. "We're going to qualify for the last 16. The next stage could be very tough, maybe tougher than the group," Herrera said referring to a potential meeting with holders Spain, the Netherlands or Chile from Group B which also includes Australia. "The four teams that can lift the trophy are Brazil, Spain, Argentina and Germany," Herrera added. "The dark horses could be Belgium because they look solid, but the biggest surprise will come from Mexico," he predicted with a deadly serious expression on his face. (Writing by Rex Gowar in Buenos Aires; Editing by Greg Stutchbury and Mike Collett)