
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 function $f(x) = \sqrt{3}\sin x \cos x - \cos^2 x + \frac{1}{2}$.

(1) Find the smallest positive period of $f(x)$ and the equation of the axis of symmetry.

(2) In $\triangle ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$, respectively. If $f\left(\frac{A}{2}\right) = \frac{1}{2}$ and $bc = 6$, find the minimum value of $a$.

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