
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 following equations:
\[
a + b + c = 3,
\]
\[
a^2 + b^2 + c^2 = 5,
\]
\[
a^3 + b^3 + c^3 = 7,
\]
find \(a^4 + b^4 + c^4\).

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