
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, if \( AC = \sqrt{2} \), \( AB = 2 \), and \(\frac{\sqrt{3} \sin A + \cos A}{\sqrt{3} \cos A - \sin A} = \tan \frac{5\pi}{12}\), then \( BC \) = _____

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