
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 $\overrightarrow{a}$ and $\overrightarrow{b}$ are two non-parallel vectors, and $\overrightarrow{AB} = \lambda_1 \overrightarrow{a} + \overrightarrow{b}$, $\overrightarrow{AC} = \overrightarrow{a} + \lambda_2 \overrightarrow{b}$, where $\lambda_1, \lambda_2 \in \mathbb{R}$, determine the necessary and sufficient condition for points A, B, and C to be collinear.

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