
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 angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, with $a=4$, $\cos A= \frac{3}{4}$, $\sin B= \frac{5\sqrt{7}}{16}$, and $c>4$.
(1) Find the length of $b$.
(2) It is known that the radius $r$ of the incircle of triangle $ABC$ is given by $r= \frac{2S}{l}$, where $S$ is the area of triangle $ABC$ and $l$ is the perimeter of the triangle. Calculate the area of the incircle of triangle $ABC$.

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