
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 parabola $y^{2}=2px(p > 0)$ and a point $M(1,m)$ on it, the distance from $M$ to its focus is $5$. Let the hyperbola $\frac{x^{2}}{a}-\frac {y^{2}}{a^2}=1$ have its left vertex at point $A$. If one of the asymptotes of the hyperbola is perpendicular to line $AM$, find the value of the real number $a$.

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