
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 that $\overrightarrow{a}$ and $\overrightarrow{b}$ are two non-collinear vectors, $\overrightarrow{AB} = 2\overrightarrow{a} + p\overrightarrow{b}$, $\overrightarrow{BC} = \overrightarrow{a} + \overrightarrow{b}$, $\overrightarrow{CD} = \overrightarrow{a} - 2\overrightarrow{b}$, if points $A$, $B$, and $D$ are collinear, then the value of the real number $P$ is $\_\_\_\_\_\_$.

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