
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 two distinct numbers $a$ and $b$, we define $\min \{a, b\}$ as the smaller value between $a$ and $b$, where $a \neq 0$. For example, $\min \{2, 3\} = 2$. According to this rule, the solution to the equation $\min \left\{\frac{1}{1-x}, \frac{2}{1-x}\right\} = \frac{2}{x-1} - 3$ is ____.

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