
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 $ABC$, such that $\overrightarrow {AP}=\lambda \overrightarrow {AB}+\mu \overrightarrow {AC}$, 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}
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