
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 space vectors $\overrightarrow{a}=(2,1,-3)$, $\overrightarrow{b}=(-1,2,3)$, $\overrightarrow{c}=(7,6,z)$, if the three vectors $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$ lie in the same plane, then the real number $z=\_\_\_\_\_\_$.

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