
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 $ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$, respectively. Given that $a\cos B = 4$ and $b\sin A = 3$.

(I) Find $\tan B$ and the value of side $a$;

(II) If the area of triangle $ABC$ is $S = 9$, find the perimeter of triangle $ABC$.

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