
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 the vector $\overrightarrow{a} = (3, -4)$, find:  
(1) The unit vector $\overrightarrow{b}$ parallel to $\overrightarrow{a}$;  
(2) The unit vector $\overrightarrow{c}$ perpendicular to $\overrightarrow{a}$;  
(3) The coordinates of the vector $\overrightarrow{e}$ obtained by rotating $\overrightarrow{a}$ 45° counterclockwise around the origin.

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