
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 sequence $\left\{a_{n}\right\}$ satisfies the conditions: $a_{1}=1$, $\frac{a_{2k}}{a_{2k-1}}=2$, $\frac{a_{2k+1}}{a_{2k}}=3$, for $k \geq 1$. What is the sum of the first 100 terms, $S_{100}$?

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