
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
Given triangle ABC, where sides $a$, $b$, and $c$ correspond to angles A, B, and C respectively, and $b=2$, $\cos{A}=-\frac{4}{5}$.
(I) If $a=4$, find the value of $\sin{B}$.
(II) If the area of triangle ABC, $S=6$, find the values of $a$ and $c$.

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