
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
Let the side lengths of triangle \( \triangle ABC \) be \(\alpha, \beta, \gamma\), and the distances from its centroid to each vertex be \(\lambda, \mu, v\). Find the value of \(\frac{\alpha^2 + \beta^2 + \gamma^2}{\lambda^2 + \mu^2 + v^2}\).

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