
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
a) Express the condition for the perpendicularity of two vectors if their coordinates are known: $\overrightarrow{r_{1}}\left(x_{1} ; y_{1}\right), \overrightarrow{r_{2}}\left(x_{2} ; y_{2}\right)$.

b) What formula expresses the distance between the points with the same coordinates? How can you calculate the angle between $\vec{r}_{1}$ and $\vec{r}_{2}$?

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