
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 triangle \( \triangle ABC \) with sides \( a, b, \) and \( c \), let \( m_a, m_b, \) and \( m_c \) represent the lengths of the medians to sides \( BC, CA, \) and \( AB, \) respectively. Find the minimum value of \( \frac{m_a^2}{a^2} + \frac{m_b^2}{b^2} + \frac{m_c^2}{c^2} \).

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