
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 $\{a_n\}$ that satisfies: $(a_1=1)$, $(a_{n+1}=3a_n,n\in N_+)$.

(I) Find the general term formula and the sum of the first $n$ terms $(S_n)$;

(II) It is known that $\{b_n\}$ is an arithmetic sequence, $T_n$ is the sum of the first $n$ terms, and $(b_1=a_2)$, $(b_3=a_1+a_2+a_3)$, find $(T_{20})$

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