
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
Find all numbers \( t \) for which exactly one of the following two statements is true:

A) The equation \( x^{2}+(t+1)x+1=0 \) has two distinct positive roots;

B) The inequality \( 4x^{2}+(t-2)x+1 \geq 0 \) holds for all positive \( x \).

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