
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 an ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$ and a hyperbola $\dfrac{x^2}{4}-\dfrac{y^2}{5}=1$ share common foci $F_1$ and $F_2$, and $P$ is an intersection point of the two curves, calculate the value of $|PF_1|\cdot|PF_2|$.

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