
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 $$p: \exists x \in [0, \frac{\pi}{2}], \cos^2 x + 2\cos x - a = 0$$; proposition $q: \forall x \in \mathbb{R}, x^2 + 2ax - 8 + 6a \geq 0$. If either proposition $p$ or $q$ is true, but not both, find the range of the real number $a$.

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