
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 cousin and I both have different amounts of homework. I work at a rate of $p$ problems per hour and it takes me $t$ hours to finish my homework, yielding $n$ problems. My cousin works at a rate of $3p - 5$ problems per hour and takes $\frac{t + 3}{2}$ hours to finish his homework. Assuming $p$ and $t$ are positive integers and I do a minimum of 15 problems per hour, how many problems does my cousin do?

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