
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
I completed my math homework in $t$ hours, working at a rate of $p$ problems per hour. My friend completed the same homework in $t-1$ hour, working at a rate of $2p-2$ problems per hour. Assume $p$ and $t$ are positive integers and I did more than $10$ problems per hour. How many problems did I complete?

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