
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 real numbers \( p \) and \( q \), the notation \( \min \{p, q\} \) represents the smaller of the two numbers \( p \) and \( q \), such as \( \min \{1, 2\} = 1 \). If \( \min \left\{\frac{1}{2} + x, x^{2}\right\} = 1 \), then \( x = \) ?

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