
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
Let F_1 and F_2 be the two foci of the hyperbola C: \dfrac{x^{2}}{9}- \dfrac{y^{2}}{m}=1, and point P is on C such that \overrightarrow{PF_1}\cdot\overrightarrow{PF_2}=0. If the directrix of the parabola y^2=16x passes through one of the foci of the hyperbola C, calculate the value of | \overrightarrow{PF_1}| \cdot | \overrightarrow{PF_2}|.

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