
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 \( a_{i}, b_{i} (i=1,2,\cdots,n) \) be rational numbers such that for any real number \( x \), \( x^{2} + x + 4 = \sum_{i=1}^{n} (a_{i} x + b_{i})^{2} \). Find the smallest possible value of \( n \).

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