
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
A real number  $ to $  is randomly and uniformly chosen from the  $ [- 3,4] $  interval. What is the probability that all roots of the polynomial  $ x ^ 3 + ax ^ 2 + ax + 1 $  are real?

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