
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 a regular hexagon \( ABCDEF \). It is known that \( \overrightarrow{AB}=\vec{a} \) and \( \overrightarrow{AF}=\vec{b} \). Find the vectors \( \overrightarrow{AD} \), \( \overrightarrow{BD} \), \( \overrightarrow{FD} \), and \( \overrightarrow{BM} \), where \( M \) is the midpoint of the side \( EF \).

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