
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 parallelogram $ABCD$, $\overrightarrow {AB} = \overrightarrow {a}$, $\overrightarrow {AD} = \overrightarrow {b}$, $\overrightarrow {AN} = 3 \overrightarrow {NC}$, and $M$ is the midpoint of $BC$. Then, $\overrightarrow {MN} = $ ______ (expressed in terms of $a$ and $b$).

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