
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  $a$ ,  $b$ ,  $c$ ,  $d$  be complex numbers satisfying
\begin{align*}
  5 &= a+b+c+d 
  125 &= (5-a)^4 + (5-b)^4 + (5-c)^4 + (5-d)^4 
  1205 &= (a+b)^4 + (b+c)^4 + (c+d)^4 + (d+a)^4 + (a+c)^4 + (b+d)^4 
  25 &= a^4+b^4+c^4+d^4
\end{align*}
Compute  $abcd$ .

*Proposed by Evan Chen*

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