
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
Solve the following system for real  $a , b, c, d, e$ : \[ \left\{ \begin{array}{ccc} 3a & = & ( b + c+ d)^3  3b & = & ( c + d +e ) ^3  3c & = & ( d + e +a )^3  3d & = & ( e + a +b )^3  3e &=& ( a + b +c)^3. \end{array}\right.  \]

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