
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
Given that the midpoint of side $BC$ of triangle $\triangle ABC$ is $D$, point $E$ lies in the plane of $\triangle ABC$, and $\overrightarrow{CD}=3\overrightarrow{CE}-2\overrightarrow{CA}$, if $\overrightarrow{AC}=x\overrightarrow{AB}+y\overrightarrow{BE}$, then determine the value of $x+y$.

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