
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 $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and $B$ is an acute angle. If $\frac{\sin A}{\sin B} = \frac{5c}{2b}$, $\sin B = \frac{\sqrt{7}}{4}$, and $S_{\triangle ABC} = \frac{5\sqrt{7}}{4}$, find the value of $b$.

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