Trulli took Toyota's first pole position in F1
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Toyota believe they can grab third place in the constructors' championship before the Formula One season ends.
The team go into next Sunday's Japanese Grand Prix at Suzuka 17 points behind struggling Ferrari, with only the Shanghai race on 16 October to follow.
Driver Jarno Trulli said: "We have made very significant progress this year to be challenging for a top-three finish in the manufacturers' championship."
"We go to Suzuka with much higher aims - we even have a chance of a podium."
Trulli took provisional pole position at Suzuka last year, only to slip down the order in qualifying.
Earlier this season, he sealed his team's first pole start at the US Grand Prix but Toyota and several other teams refused to race on tyre safety grounds.
However, Toyota's best chance of success could rest with the Italian's team-mate, Ralf Schumacher, who made his name in Japan before graduating to F1.
"Local knowledge can come in handy, especially if there is a wet race, as you can predict which areas of the track will dry the quickest," said the German.
"We will certainly be aiming to bring home some more points and who knows? Perhaps we can even make it to the podium."