
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
For $n$ vectors, $\overrightarrow{a_1}, \overrightarrow{a_2}, \ldots, \overrightarrow{a_n}$, if there exist $n$ non-zero real numbers $k_1, k_2, \ldots, k_n$ such that $k_1\overrightarrow{a_1} + k_2\overrightarrow{a_2} + \ldots + k_n\overrightarrow{a_n} = \overrightarrow{0}$ holds, then the vectors $\overrightarrow{a_1}, \overrightarrow{a_2}, \ldots, \overrightarrow{a_n}$ are said to be linearly dependent. According to this rule, the values of real numbers $k_1, k_2, k_3$ that make the vectors $\overrightarrow{a_1} = (1, 0), \overrightarrow{a_2} = (1, -1), \overrightarrow{a_3} = (2, 2)$ linearly dependent are \_\_\_\_\_\_ . (Only one set of values needs to be provided)

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