
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 $x^{2}- \frac{y^{2}}{4}=1$ with its right focus $F$, a line passing through point $F$ and parallel to one asymptote of the hyperbola intersects the hyperbola at point $P$. Point $M$ lies on line $PF$ and satisfies $\overrightarrow{OM}\cdot \overrightarrow{PF}=0$. Determine the value of $\frac{|\overrightarrow{PM}|}{|\overrightarrow{PF}|}$.

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