
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
(10 points) (Fall 2014, Zhengzhou Final Exam) Proposition p: The inequality $x^2+2ax+4>0$ holds for all $x \in \mathbb{R}$. Proposition q: The focus of the parabola $y^2=4ax$ is to the left of $(1,0)$. If $p \lor q$ is true and $p \land q$ is false, find the range of the real number $a$.

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