
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 equation $x^2-ax+1=0$ has real roots; proposition $q$: For any $x \in [-1,1]$, the inequality $a^2-3a-x+1 \leqslant 0$ always holds. If "$p \wedge q$" is a false proposition, and "$\neg q$" is also a false proposition, find the range of the real number $a$.

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