
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
Let the sequence $\{a_n\}$ be defined by the formula $a_n=3^n$ ($n\in\mathbb{N}^*$). The sequence $\{b_n\}$ is defined as follows: for $m\in\mathbb{N}^*$, $b_m$ is the term of sequence $\{a_n\}$ such that $n=3m$. Then, $b_3= \boxed{\_\_\_\_\_\_}$; the sum of the first $m$ terms of sequence $\{b\}$, $S_m= \boxed{\_\_\_\_\_\_}$.

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