
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), and C(2, 1), and P is a point on plane ABC, $\overrightarrow{AP} = \lambda \overrightarrow{AB} + \mu \overrightarrow{AC}$, 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 $\lambda + \mu$.

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