
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
Find all real  $a,b,c,d,e,f$  that satisfy the system
 $4a = (b + c + d + e)^4$ 
 $4b = (c + d + e + f)^4$ 
 $4c = (d + e + f + a)^4$ 
 $4d = (e + f + a + b)^4$ 
 $4e = (f + a + b + c)^4$ 
 $4f = (a + b + c + d)^4$ 

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