
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 a parabola $y^{2}=2px(p > 0)$ with a point $M(1,m)$ on it, the distance from $M$ to its focus is $5$. The left vertex of the hyperbola $C: x^{2}-\frac{y^{2}}{b^{2}}=1 (b > 0)$ is $A$, and if one of the asymptotes of the hyperbola $C$ is perpendicular to the line $AM$, then its eccentricity is __________.

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