
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 condition $p$: $\exists x \in \mathbb{R}$, such that ${x}^{2}-2x\leqslant {a}^{2}-a-3$ holds, and condition $q$: the function $f(x)=(5-2a)^{x}$ is decreasing on $\mathbb{R}$. If "$p \lor q$" is a true statement, and "$p \land q$" is a false statement, find the range of the real number $a$.

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