
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 $\{a_n\}$ that satisfies: 
$$
a_n=
\begin{cases}
2n, & n=2k-1 \\
2^{n-1}, & n=2k
\end{cases}
\quad (k\in\mathbb{N}^*)
$$
If sequence $\{b_n\}$ satisfies $b_n=a_{3n}$, and the sum of the first $10$ terms of sequence $\{b_n\}$ is $S_{10}$, then the value of $63S_{10}-2^{35}$ is ______.

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