
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 $P$: "For any $x \in [1,2]$, $x^{2}-a \geqslant 0$", and proposition $Q$: "There exists $x \in \mathbb{R}$, $x^{2}+(a-1)x+1 < 0$". If "P or Q" is true, and "P and Q" is false, find the range of the real number $a$.

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