
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
The sum of the first $99$ terms of the sequence $1$, $1+2$, $1+2+2^2$, $\ldots$, $1+2+2^2+\ldots+2^{n-1}$, $\ldots$ is equal to $2^{100}-101$.

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