
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
Let proposition P be: $x_1$, $x_2$ are the two real roots of the equation $x^2-ax-2=0$, and the inequality $|m^2-5m-3| \geq |x_1-x_2|$ holds for any real number $a \in [-1, 1]$. Proposition Q is: the range of the function $f(x) = \log(4x^2+(m-2)x+1)$ is all real numbers. If both P and Q are true, find the range of the real number $m$.

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