
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
A necklace consists of 30 blue and some number of red beads. It is known that on either side of each blue bead there are beads of different colors, and every other bead from each red one is also of different colors. How many red beads can there be in this necklace? (The beads in the necklace are arranged cyclically, meaning the last one is adjacent to the first one.)

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