
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 $\{a_n\}$ satisfies 
$$
a_n= 
\begin{cases} 
\frac{a_{n-1}}{2}, & \text{if } a_{n-1} \text{ is even} \\
3a_{n-1}+1, & \text{if } a_{n-1} \text{ is odd}
\end{cases}
$$
If $a_1=34$, then the sum of the first $100$ terms of the sequence $\{a_n\}$ is ______.

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