
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 an acute-angled triangle \( \triangle ABC \) with sides \( a \), \( b \), and \( c \) opposite the angles \( A \), \( B \), and \( C \) respectively, if \( 2a^{2} = 2b^{2} + c^{2} \), what is the minimum value of \( \tan A + \tan B + \tan C \)?

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