
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
My friend and I both have math homework: we need to solve a certain number of problems. I solve problems at a rate of $p$ problems per hour and it takes me $t$ hours to finish my homework. My friend works at a rate of $2p-6$ problems per hour and it takes him $t-2$ hours to finish his homework. I know $p$ and $t$ are positive integers and I solve more than $10$ problems per hour. How many problems did I solve?

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