
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 vectors $\overline{a}$ and $\overline{b}$ be non-collinear. If $\overline{AB}=2\overline{a}+p\overline{b}$, $\overline{BC}=\overline{a}+\overline{b}$, and $\overline{CD}=\overline{a}-2\overline{b}$, and points A, B, and D are collinear, determine the value of the real number $p$.

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