
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
There are three types of tickets at the children's park amusement area: type A tickets cost 7 yuan, type B tickets cost 4 yuan, and type C tickets cost 2 yuan. One day, the amusement area sold a total of 85 tickets and earned an income of 500 yuan, with type A tickets selling 31 more than type B tickets. How many type A tickets were sold?

Present the answer in LaTex format: \boxed{Your answer}
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