
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 that in $\triangle ABC$, the three internal angles $A$, $B$, and $C$ correspond to the sides $a$, $b$, and $c$ respectively, and $\cos(\frac{\pi}{4} - A) = \frac{\sqrt{2}}{10}$.

(I) Find the value of $\sin(A)$;
(II) If the area of $\triangle ABC$ is $S = 12$, and $b = 6$, find the value of $a$.

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