
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
If point O is any point in space, and any three of the points A, B, C, D are not collinear, and these four points are in the same plane, and $\overrightarrow{OC} = \lambda \overrightarrow{OA} + \mu \overrightarrow{OB}$ with $\lambda + \mu = 1$, determine the value of $x + y + z$ if $\overrightarrow{OD} = x \overrightarrow{OA} + y \overrightarrow{OB} + z \overrightarrow{OC}$.

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