
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Angles $A$, $B$, $C$ form an arithmetic sequence, $c - a = 1$, and $b = \sqrt{7}$.

(I) Find the area $S$ of $\triangle ABC$.

(II) Find the value of $\sin\left(2C + \frac{\pi}{4}\right)$.

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