
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 the parabola, the distance from point $M$ to the focus of the parabola is $5$. The left vertex of the hyperbola $x^{2}- \dfrac {y^{2}}{a}=1$ is $A$. If one asymptote of the hyperbola is perpendicular to line $AM$, determine the real number $a$.

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