
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 on a plane: $A(1,0)$, $B(0,1)$, and $C(2,5)$.

1. Find the magnitude of the vector $2\overrightarrow{AB} + \overrightarrow{AC}$.
2. Find the cosine value of the angle between vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$.
3. Find the coordinates of the unit vector perpendicular to $\overrightarrow{BC}$.

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