
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 $\triangle ABC$, the sides opposite to angles A, B, and C are denoted as $a$, $b$, and $c$, respectively. The function $f(x) = \sin(2x + A)$.
(1) If $A = \frac{\pi}{2}$, then the value of $f\left(-\frac{\pi}{6}\right)$ is _________;
(2) If $f\left(\frac{\pi}{12}\right) = 1$, $a = 3$, and $\cos B = \frac{4}{5}$, find the length of side $b$ of triangle $\triangle ABC$.

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