
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 trapezoid $ABCD$, $AD // BC$ and $\angle B=40^{\circ}$, $\angle C=50^{\circ}$. Points $E, M, F, N$ are the midpoints of $AB$, $BC$, $CD$, and $DA$ respectively. If $EF = a$ and $MN = b$, then calculate $BC$.

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