
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 $\overrightarrow{a}, \overrightarrow{b}$ are base vectors, and vectors $\overrightarrow{AB}= \overrightarrow{a}-k \overrightarrow{b}$, $\overrightarrow{CB}=2 \overrightarrow{a}+ \overrightarrow{b}$, $\overrightarrow{CD}=3 \overrightarrow{a}- \overrightarrow{b}$, find the value of the real number $k$ if points $A$, $B$, $D$ are collinear.

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