
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
Consider the set of all equations \( x^4 + a_3x^3 + a_2x^2 + a_1x + a_0 = 0 \), where \( a_3, a_2, a_1, a_0 \) are real constants and \( |a_i| \leq 3 \) for \( i=0,1,2,3 \). Let \( r \) be the largest positive real number which satisfies at least one of these equations. Determine the range of \( r \).
**A)** \( 2 < r < 3 \)  
**B)** \( 3 < r < 4 \)  
**C)** \( r = 3 \)  
**D)** \( r = 4 \)  
**E)** \( 5 < r < 6 \)

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