
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 the acute triangle \( \triangle ABC \), if
\[ \sin A = 2 \sin B \cdot \sin C, \]
find the minimum value of \( \tan A + 2 \tan B \cdot \tan C + \tan A \cdot \tan B \cdot \tan C \).

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