
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 vectors on a plane, where $\overrightarrow{a}=(1,2)$.

(1) If vector $\overset{⇀}{c}$ is a unit vector and is collinear with $\overset{⇀}{a}$, find the coordinates of vector $\overset{⇀}{c}$.

(2) If $|\overrightarrow{b}|=\sqrt{5}$, and $2\overrightarrow{a}+\overrightarrow{b}$ is perpendicular to $2\overrightarrow{a}-3\overrightarrow{b}$, find the cosine value of the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$.

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