
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 $a = (1,2)$, $b = (-2, n)$ (where $n > 1$), and the angle between $a$ and $b$ is 45°.

(1) Find $b$;  
(2) If $c$ is in the same direction as $b$, and $a$ is perpendicular to $c - a$, find $c$.

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