
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
Determine the range of t such that the quadratic function \( y = -x^2 + 6x - 7 \) has a maximum value of \( y_{\text{max}} = -(t-3)^2 + 2 \) when \( x \) is in the range \( t \leq x \leq t+2 \).

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