
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 $C$ is a geometric sequence starting at 3 with a common ratio of 3. Sequence $D$ is an arithmetic sequence starting at 15 with a common increment of 15. Each sequence stops as soon as one of its terms exceeds $450$. What is the least positive difference between a number selected from sequence $C$ and a number selected from sequence $D$?

$\bullet$ Sequence $C:$ $3,$ $9,$ $27,$ $81,$ $243,$ $\ldots$

$\bullet$ Sequence $D:$ $15,$ $30,$ $45,$ $60,$ $75,$ $\ldots$

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