
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
Given that $P_1(a, b_1)$ and $P_2(2, b_2)$ are two distinct points on the line $y = kx + 1$ (where $k$ is a constant), find the condition for the system of equations
$$
\begin{cases}
a_1 x + b_1 y = 1 \\
a_2 x + b_2 y = 1
\end{cases}
$$
to have solutions.

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