
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 real numbers \(a, b, c\) satisfying \(a + b + c = 1\), \(a^{2} + b^{2} + c^{2} = 2\), and \(a^{3} + b^{3} + c^{3} = 3\), find the values of \(abc\) and \(a^{4} + b^{4} + c^{4}\).

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