
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 $\triangle ABC$, points $M$ and $N$ satisfy $\overline{AM} = 2\overline{MC}$, $\overline{BN} = \overline{NC}$. If $\overline{MN} = x\overline{AB} + y\overline{AC}$, then $x = \_\_\_\_\_\_$, $y = \_\_\_\_\_\_$.

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