
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 point $O$ is the origin, $\overrightarrow{O M}=(-1,1)$, $\overrightarrow{N M}=(-5,-5)$, set $A=\{\overrightarrow{O R} | R N \mid=2\}$, $\overrightarrow{O P}, \overrightarrow{O Q} \in A, \overrightarrow{M P}=\lambda \overrightarrow{M Q}(\lambda \in \mathbf{R}, \lambda \neq 0)$, find $\overrightarrow{M P} \cdot \overrightarrow{M Q}$.

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