
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
Sequence $A$ is a geometric sequence. Sequence $B$ is an arithmetic sequence. Each sequence stops as soon as one of its terms is greater than $200.$ 

$\bullet$ Sequence $A:$ starts at $3$ and each following term triples the previous term.

$\bullet$ Sequence $B:$ starts at $15$ and each following term increases by $15$ from the previous term. 

What is the least positive difference between a number from sequence $A$ and a number from sequence $B$?

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