
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 $p$ and $q$:
- Proposition $p$: The domain of the function $y = \log_{0.5}(x^2 + x + a)$ is $\mathbb{R}$.
- Proposition $q$: The quadratic inequality $x^2 - 2ax + 1 \leq 0$ has real solutions in $\mathbb{R}$.

Find the range of values for the real number $a$ if either proposition $p$ is true and $q$ is false, or if proposition $p$ is false and $q$ is true.

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