
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 triangle $\triangle ABC$, $\overrightarrow{AM}=\frac{3}{4}\overrightarrow{AB}+\frac{1}{4}\overrightarrow{AC}$ and $\overrightarrow{CN}=\frac{1}{2}\overrightarrow{CB}+\frac{1}{2}\overrightarrow{CA}$. $AM$ intersects $CN$ at point $P$ and $\overrightarrow{AP}=x\overrightarrow{AB}+y\overrightarrow{AC}$ ($x,y∈R$). Find $x+y$.

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