
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 propositions $p$: $2 < 3c$ and $q$: $\forall x \in \mathbb{R}, 2x^2 + 4cx + 1 > 0$, with either $p \lor q$ or $p \land q$ being true, determine the range of values for the number $c$.

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