
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 the sequence $\{a_n\}$, where $a_n= \begin{cases}2^{n-1} & (n\text{ is an odd positive integer}) \\ 2n-1 & (n\text{ is an even positive integer})\end{cases}$, find $a_9=$ ______ (answer in digits), and let the sum of the first $n$ terms of $\{a_n\}$ be $S_n$, then find $S_9=$ ______ (answer in digits).

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