
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
Numbers \( a_{1}, b_{1}, a_{2}, b_{2}, \ldots, a_{n}, b_{n} \) satisfy the conditions

\[ 
\begin{gathered}
a_{1}^{2} + a_{2}^{2} + \cdots + a_{n}^{2} = 2018^{2}, \quad b_{1}^{2} + b_{2}^{2} + \cdots + b_{n}^{2} = 2017^{2} \\
a_{1} b_{1} + a_{2} b_{2} + \cdots + a_{n} b_{n} = 2017 \cdot 2018
\end{gathered}
\]

Find the ratios \( a_{1} / b_{1}, a_{2} / b_{2}, \ldots, a_{n} / b_{n} \).

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