
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 non-zero vectors $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$ lie in the same plane. Write down a set of vectors that satisfy the equation $(\overrightarrow{a} \cdot \overrightarrow{b})\overrightarrow{c} = \overrightarrow{a}(\overrightarrow{b} \cdot \overrightarrow{c})$. The coordinates of vectors $\overrightarrow{a}$ and $\overrightarrow{c}$ are ____.

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