
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 $\{a_n\}$, the first term $a_1=1$, and sequence $\{b_n\}$ satisfies $b_n=\left(\frac{1}{2}\right)^{a_n}$, $b_1b_2b_3=\frac{1}{64}$.  
(I) Find the general term of the sequence $\{a_n\}$.  
(II) Find the condition such that $a_1b_1+a_2b_2+\ldots+a_nb_n<2$.

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