
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
In quadrilateral $ABCD$, let $\overrightarrow{AB} = \vec{a}$ and $\overrightarrow{CD} = \vec{b}$. Points $E$ and $F$ are the midpoints of $AC$ and $BD$, respectively. Express the vector $\overrightarrow{EF}$ using $\vec{a}$ and $\vec{b}$.

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