
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
The ratio of the number of red beads on a chain to the number of yellow beads is the same as the ratio of the number of yellow beads to the number of blue beads. There are 30 more blue beads than red ones. How many red beads could be on the chain?

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