
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 with sides a, b, and c opposite to angles A, B, and C respectively, and b = a(cosC - sinC).

1. Find angle A.
2. If $a = \sqrt{10}$ and $\sin B = \sqrt{2} \sin C$, find the area of triangle ABC.

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