
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 points $O(0,0)$, $A(1,1)$, $B(-1,0)$.  
$(1)$ If $\overrightarrow{OC}=\overrightarrow{OA}+λ\overrightarrow{OB}$, where $\lambda$ is a real number, and $\overrightarrow{OC}⊥\overrightarrow{AB}$, find the value of $\lambda$.  
$(2)$ Find the cosine value of the angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$.

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