
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 the volume  $V$  of the solid formed by a rotation of the region enclosed by the curve  $y=2^{x}-1$  and two lines  $x=0,\ y=1$  around the  $y$  axis.

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