
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 two non-collinear plane vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, vector $\overrightarrow{AB} = \lambda \overrightarrow{a} + \overrightarrow{b}$, $\overrightarrow{AC} = \overrightarrow{a} - \mu \overrightarrow{b}$ ($\lambda, \mu \in \mathbb{R}$). If $\overrightarrow{AB} \parallel \overrightarrow{AC}$, find the relationship between $\lambda$ and $\mu$.

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