
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
Let $k$ be a nonzero constant. If $\frac{xy}{k(x+y)} = a$, $\frac{xz}{k(x+z)} = b$, and $\frac{yz}{k(y+z)} = c$, determine the value of $x$ in terms of $a$, $b$, $c$, and $k$.

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