
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 that $F\_1$ and $F\_2$ are the left and right foci of the hyperbola $C$: $\frac{x^2}{9} - \frac{y^2}{27} = 1$, and point $A$ is on $C$. Point $M$ has coordinates $(2, 0)$, and $AM$ is the bisector of $\angle F\_1AF\_2$. Find the length of $|AF\_2|$.

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