
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 $\triangle ABC$, $AD = DB$, $AE = \frac{1}{2} EC$, and $CD$ intersects $BE$ at point $F$. Let $\overrightarrow{AB}=\overrightarrow{a}$, $\overrightarrow{AC}=\overrightarrow{b}$, and $\overrightarrow{AF}=x\overrightarrow{a}+y\overrightarrow{b}$. Find the ordered pair $(x, y)$.

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