
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
Given proposition p: The function y = kx + 1 is an increasing function on R, and proposition q: The function y = x^2 - 2x + 3 has a maximum value of 3 and a minimum value of 2 on the interval [0, k]. If p ∧ q is a false proposition, and p ∨ q is a true proposition, find the range of values for k.

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