
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 that the sequence $\{a_n\}$ is an arithmetic sequence, and $\{b_n\}$ is a geometric sequence, with $a_1=b_1=2$, $b_4=54$, and $a_1+a_2+a_3=b_2+b_3$,

(1) Find the general formula for the sequence $\{b_n\}$;

(2) Find the sum of the first 10 terms of the sequence $\{a_n\}$, denoted as $S_{10}$.

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