
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 the line $y=-2x$ passes through the point $P(-2,a)$, and the point $P$ is symmetric with respect to the $y$-axis to the point $P'$ on the graph of the inverse proportion function $y=\frac{k}{x}$ (where $k\neq 0$), find the expression of the inverse proportion function.

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