
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 three points $A(1,-1)$, $B(3,0)$, $C(2,1)$, and $P$ is a point on the plane $ABC$, with $\overrightarrow{AP}=λ \overrightarrow{AB}+μ \overrightarrow{AC}$, and $\overrightarrow{AP} \cdot \overrightarrow{AB}=0$, $\overrightarrow{AP} \cdot \overrightarrow{AC}=3$.

(1) Find $\overrightarrow{AB} \cdot \overrightarrow{AC}$;

(2) Find the value of $λ+μ$.

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