
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
Real numbers  $x,y,a$  satisfy the equations  $x+y = x^3 +y^3 = x^5 +y^5 = a$ .
Find all possible values of  $a$ .

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