
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 \( a, b, c, d, e \) be five numbers satisfying the following conditions:
\[
\begin{array}{l}
a+b+c+d+e=0, \quad \text{and} \\
abc+abd+abe+acd+ace+ade+bcd+bce+bde+cde=2008.
\end{array}
\]

Find the value of \( a^{3}+b^{3}+c^{3}+d^{3}+e^{3} \).

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