
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 hyperbola $\dfrac{x^2}{6} - \dfrac{y^2}{3} = 1$ with foci $F_1$, $F_2$, and a point $M$ on the hyperbola such that $M F_1 \perp x$-axis, calculate the distance from $F_1$ to the line $F_2 M$.

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