
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 propositions p and q:   
p: The equation $x^2 - ax + 1 = 0$ has real roots.  
q: for any $x \in [-1, 1]$, the inequality $a^2 - 3a - x + 1 \leq 0$ always holds,   
if the proposition "$p \land q$" is false and the proposition "$\lnot q$" is also false, find the range of the real number $a$.

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