
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
Given point $P$ on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{9} = 1$, one asymptote of the hyperbola is $3x - 2y = 0$, and $F\_1$, $F\_2$ are the left and right foci of the hyperbola, respectively. If $|PF\_1| = 3$, find $|PF\_2| =$ $\_\_\_\_\_\_\_\_\_\_\_$.

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