
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
Given a sequence $\{a_n\}$, and $a_1$, $\frac{a_2}{a_1}$, $\frac{a_3}{a_2}$, ..., $\frac{a_n}{a_{n-1}}$ form a geometric sequence with the first term being $1$ and the common ratio being $2$, calculate $a_{101}$.

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