
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 $M(1,t) (t > 0)$ on it, the distance from point $M$ to the focus is $5$. For a hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1 (a > 0)$ with its left vertex at $A$, if one of the hyperbola's asymptotes is parallel to line $AM$, find the value of real number $a$.

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