
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 $x_1$ and $x_2$ be the two real roots of the equation $ax^2+bx+1=0$, and $x_3$ and $x_4$ be the two real roots of the equation $a^2x^2+bx+1=0$. If $x_3 < x_1 < x_2 < x_4$, then the range of the real number $a$ is.

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