
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
There is a box containing many pieces of wood, which are red, white, and blue. The number of blue pieces is at least half the number of white pieces and at most one-third the number of red pieces. The sum of the number of white and blue pieces is at least 55. Determine the minimum number of red pieces.

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