
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 lengths of the sides opposite to angles A, B, and C are a, b, and c respectively, and b = 3, c = 1, and A = 2B.
(1) Find the value of a;
(2) Find the value of sin(A + $\frac{\pi}{4}$).

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