
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 the operation $f$ defined for rational numbers $a, b, c$ such that $f(a, b, c) = a^2 + 2bc$, find the value of $f(1, 23, 76) + f(23, 76, 1) + f(76, 1, 23)$.

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