
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 proposition p: If there exists a positive number $x \in (2, +\infty)$ such that $2^x(x-a) < 1$ holds, and proposition q: The function $y = \lg(x^2+2ax+a)$ has a range of $\mathbb{R}$, if $p \land q$ is a false proposition and $p \lor q$ is a true proposition, find the range of the real number $a$.

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