
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 a triangle $ABC$ with sides $a$, $b$, and $c$ opposite angles $A$, $B$, and $C$ respectively, and the condition $a\sin A + b\sin B = c\sin C + \sqrt{2}a\sin B$:
(I) Find angle $C$.
(II) Find the maximum value of $\sqrt{3}\sin A - \cos\left(B + \frac{\pi}{4}\right)$.

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