
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 $\overrightarrow{m} = (\frac{1}{2}\sin x, \frac{\sqrt{3}}{2}), \overrightarrow{n} = (\cos x, \cos^2x - \frac{1}{2}) (x \in R)$, and the function $f(x) = \overrightarrow{m} \cdot \overrightarrow{n}$.
1. Find the equation of the axis of symmetry for $f(x)$.
2. In an acute triangle $ABC$, where the sides opposite angles $A, B, C$ are $a, b, c$ respectively, if $f(A) = 0, \sin B = \frac{4}{5}, a = \sqrt{3}$, find the value of $b$.

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