
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 an arithmetic sequence $\{a_n\}$ and a geometric sequence $\{b_n\}$, where $a_1=b_1=1$, $a_2=b_2$, and $a_4+2=b_3$.

(I) Find the general term formulas for sequences $\{a_n\}$ and $\{b_n\}$.

(II) If $a_m=b_n$ (n∈N*), write down the relationship between m and n as $m=f(n)$, and calculate $f(1)+f(2)+…+f(n)$.

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