
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 graph of the second function is the inverse of \( \varphi(x) \) and its graph is symmetric to the graph of the third function with respect to the line \( x+y=0 \), find the equation of the third function.

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