
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
Given that $P$ philosophy books, $A$ algebra books, and $G$ geometry books, where the thickness of an algebra book is half the thickness of a philosophy book and the thickness of a geometry book is twice the thickness of an algebra book, completely fill a shelf, and $J$ algebra books and $K$ geometry books alone would fill the same shelf, find the value of $R$, where $R$ philosophy books alone would fill the shelf.

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