
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
In $\triangle ABC$, the sides opposite to angles A, B, and C are $a$, $b$, and $c$, respectively. If $$\frac{a^2}{bc} - \frac{c}{b} - \frac{b}{c} = \sqrt{3}$$, and the radius of the circumcircle of $\triangle ABC$ is 3, find $a$.

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