
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
For a function $g(x)$ defined on the interval $I$, denote $g(I) = \{y | y = g(x), x \in I\}$. Given that the function $y = f(x)$, which has a domain of $[0, 3]$, has an inverse function $y = f^{-1}(x)$, and $f^{-1}([0, 1)) = [1, 2)$, $f^{-1}((2, 4]) = [0, 1)$. If the equation $f(x) - x = 0$ has a solution $x$, then $x =$ __.

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