
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  $x, y$  such that   $\begin{cases}(1 + x)(1 + x^2)(1 + x^4) = 1+ y^7 
 (1 + y)(1 + y^2)(1 + y^4) = 1+ x^7 \end{cases}$  .

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