
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
Consider the sequence  $ (x_n)_{n\ge 0}$  where  $ x_n\equal{}2^{n}\minus{}1\ ,\ n\in \mathbb{N}$ . Determine all the natural numbers  $ p$  for which:

\[ s_p\equal{}x_0\plus{}x_1\plus{}x_2\plus{}...\plus{}x_p\]

is a power with natural exponent of  $ 2$ .

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