
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 that $O$ is the origin of coordinates, and $P$ is a point on the hyperbola $C$: $\frac{x^{2}}{9}- \frac{y^{2}}{16}=1$, and point $M$ satisfies $|\overrightarrow{OM}|=1$, and $\overrightarrow{OM}\cdot\overrightarrow{PM}=0$, determine the minimum value of the distance from point $P$ to the asymptote of the hyperbola $C$.

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