
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 hyperbola $\dfrac {x^{2}}{4}- \dfrac {y^{2}}{5}=1$, its left and right foci are $F_{1}$ and $F_{2}$, respectively. Point $P$ is a point on the hyperbola, and $\overrightarrow{F_{1}F_{2}} \cdot \overrightarrow{PF_{2}}=0$, calculate the value of $|PF_{1}|$.

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