
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 $\frac{xy}{x+y}= p$, $\frac{xz}{x+z}= q$, and $\frac{yz}{y+z}= r$ where $p, q, r$ are different from zero and $x \neq -y, x \neq -z, y \neq -z$, find the value of $x$ if $p = 3q$ and $p = 2r$.

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