
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
On the board, there were written numbers \(a\), \(b\), and \(c\). They were erased, and instead the numbers \(a^4 - 2b^2\), \(b^4 - 2c^2\), \(c^4 - 2a^2\) were written. After this, it turned out that the same numbers as initially were written on the board (possibly in a different order). Find the numbers \(a\), \(b\), \(c\) if it is known that \(a + b + c = -3\).

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