
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
Let proposition $p$: the function $y=kx+1$ is increasing on $\mathbb{R}$, and proposition $q$: there exists an $x \in \mathbb{R}$ such that $x^2 + (2k-3)x + 1 = 0$. If the proposition $p \land q$ is false and the proposition $p \lor q$ is true, determine the range of values for $k$.

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