
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 \(ABCD\), \(AB \parallel CD\) and \(AB = 2CD\). \(M\) and \(N\) are the midpoints of \(DC\) and \(AB\) respectively. Given \(\overrightarrow{AB} = \vec{a}\) and \(\overrightarrow{AD} = \vec{b}\), find \(\overrightarrow{BC}\) and \(\overrightarrow{MN}\).

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