
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
Let $O$ be the origin. Determine a scalar $k$ so that whenever points $A$, $B$, $C$, $D$, and $E$ satisfy the equation:
\[2 \overrightarrow{OA} - 3 \overrightarrow{OB} + 4 \overrightarrow{OC} + k \overrightarrow{OD} + 2 \overrightarrow{OE} = \mathbf{0},\]
the points $A, B, C, D, E$ are guaranteed to be coplanar.

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