
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
Suppose a shelf can be fully filled with \(P\) programming books (each having thickness \(t\)) or with combinations of \(B\) biology books (each of double the thickness of a programming book) and \(F\) physics books (each with triple the thickness of a programming book). Also, \(R\) programming books and \(C\) biology books together can completely fill the shelf. Finally, \(Q\) programming books alone would fill this shelf. Determine \(Q\) if \(P, B, F, R, C\) are distinct positive integers.
A) \(R + C\)
B) \(2R + C\)
C) \(R + 2C\)
D) \(P + R\)
E) \(P + 2R\)

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