
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
Let the values of $a$, $b$, $c$, $d$, $e$ be one of $0$, $1$, $2$, and satisfy $a+b+c+d+e=6$, $a^2+b^2+c^2+d^2+e^2=10$. Calculate the value of $a^3+b^3+c^3+d^3+e^3$.

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