
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. The function is $f(x)=\sin (2x+A)$.
(1) If $A=\frac{\pi}{2}$, find the value of $f(-\frac{\pi}{6})$;
(2) If $f(\frac{\pi}{12})=1$, $a=3$, $\cos B=\frac{4}{5}$, find the length of side $b$ in $\triangle ABC$.

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