
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 the ellipse $\frac{x^{2}}{m^{2}} + \frac{y^{2}}{9} = 1$ (m > 0) and the hyperbola $\frac{x^{2}}{n^{2}} - \frac{y^{2}}{4} = 1$ (n > 0) share the same foci $F_1$ and $F_2$. If point P is one of the intersection points of the ellipse and the hyperbola, find the value of $|PF_1| \cdot |PF_2|$.

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