
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 in  $\mathbb{R}$  the equation : $(x+1)^5 + (x+1)^4(x-1) + (x+1)^3(x-1)^2 +$   $ (x+1)^2(x-1)^3 + (x+1)(x-1)^4 + (x-1)^5 =$   $ 0$ .

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