
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 $ \triangle ABC $, the sides opposite angles A, B, C are respectively $ a, b, c $, with $ A = \frac{\pi}{4} $, $ \sin A + \sin(B - C) = 2\sqrt{2}\sin 2C $ and the area of $ \triangle ABC $ is 1. Find the length of side $ BC $.

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