
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
Millipede Mirka consists of a head and several segments, each with one pair of legs. When it got cold, she decided to dress up. Therefore, on the third segment from the end and then on every third segment thereafter, she put a sock on her left leg. Similarly, on the fifth segment from the end and then on every fifth segment thereafter, she put a sock on her right leg. She then found that 14 segments still had both legs bare.

Determine the total number of legs Mirka the millipede could have; specify all possibilities.

(E. Novotná)

Hint: How many segments from the end have both legs dressed first?

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