
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. Given that 4csinC = (b + a)(sinB - sinA).
(1) Can a, b, C possibly form an arithmetic sequence? Why?
(2) If b = 3c, and the perimeter of triangle ABC is 4 + $\sqrt {5}$, find the area of triangle ABC.

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