
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 randomly pick an integer $n$ between $1$ and $15$ inclusive. What is the probability that I choose an $n$ such that there exists an integer $m$ so that $n$ and $m$ satisfy the equation $nm - 6n - 3m = 3$? Express your answer as a common fraction.

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