
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
In the arithmetic sequence {a<sub>n</sub>}, a<sub>3</sub>+a<sub>4</sub>+a<sub>5</sub>=84, a<sub>9</sub>=73.
(I) Find the general term formula for the sequence {a<sub>n</sub>};
(II) For any m∈N*, let b<sub>m</sub> denote the number of terms in the sequence {a<sub>n</sub>} that fall within the interval (9<sup>m</sup>,9<sup>2m</sup>). Find the sum S<sub>m</sub> of the first m terms of the sequence {b<sub>m</sub>}.

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