
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
Rationalize the denominator of $\frac{5}{3\sqrt[4]{7}}$. The answer can be written in the form $\frac{P\sqrt[4]{Q}}{R}$, where $P$, $Q$, and $R$ are integers, $R$ is positive, and $Q$ is not divisible by the fourth power of any prime. Find $P+Q+R$.

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