
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 \( y = f(x) \) be a strictly increasing function with an inverse function \( y = g(x) \). Let \( x_1 \) and \( x_2 \) be the solutions to the equations \( f(x) + x = 2 \) and \( g(x) + x = 2 \) respectively. Find \( x_1 + x_2 \).

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