
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: The function $y=2^{x^2-2ax}$ is increasing on $x\in[1,+\infty)$; proposition q: The inequality $(a-2)x^2+2(a-2)x-4<0$ holds for any real number $x\in\mathbb{R}$, if $p\lor q$ is true, find the range of the real number $a$.

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