
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
Suppose \( a_{i}, b_{i} (i=1,2,\ldots,n) \) are rational numbers, such that for any real number \( x \), the following holds:
\[ x^{2}+x+4=\sum_{i=1}^{n}\left(a_{i} x+b_{i}\right)^{2}. \]

Find the minimum possible value of \( n \).

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