
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
Suppose \( y = f(x) \) is a function defined on the domain and range \(\mathbf{R}\), with its inverse function denoted as \( y = f^{-1}(x) \). Given that \( f(x) + f(1 - x) = 2 \) holds for all \( x \in \mathbf{R} \), find the value of \( f^{-1}(x - 2) + f^{-1}(4 - x) \).

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