
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 the real numbers $a\_1$, $a\_2$, $a\_3$, $a\_4$ that satisfy $a\_1 + a\_2 + a\_3 = 0$, $a\_1a\_4^2 + a\_2a\_4 - a\_2 = 0$, and $a\_1 > a\_2 > a\_3$, find the range of $a\_4$.

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