
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 the parallelogram $ABCD$, it is known that $E$ is the midpoint of $AB$, $F$ is the point on side $BC$ that divides it into three equal parts closer to point $B$, $AF$ and $DE$ intersect at point $M$, and $\angle DAB = \frac{π}{3}$. Let $\overrightarrow{AB} = \overrightarrow{a}$, $\overrightarrow{AD} = \overrightarrow{b}$, and $|\overrightarrow{b}| = \frac{3}{2}|\overrightarrow{a}|$.
$(1)$ Express $\overrightarrow{EF}$ in terms of $\overrightarrow{a}$ and $\overrightarrow{b}$.
$(2)$ Find $\angle EMF$.

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