
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 hyperbola $C:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\left( a>0,b>0 \right)$ with foci $F_1$ and $F_2$, a perpendicular line is drawn from $F_2$ to one of the asymptotes of $C$, with the foot of the perpendicular denoted as $M$. If the area of $\triangle MF_1F_2$ is $4a^2$, determine the equation of the asymptote of $C$.

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