
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
If $a, b, c$ are positive real numbers satisfying $a + b + c = 1$, find 
\[ f(a, b, c) = \frac{a^4}{a^3 + b^2 + c^2} + \frac{b^4}{b^3 + a^2 + c^2} + \frac{c^4}{c^3 + b^2 + a^2} \]

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