
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 vectors $\overrightarrow{a} = (3, 4)$, $\overrightarrow{b} = (9, x)$, $\overrightarrow{c} = (4, y)$, and $\overrightarrow{a} \parallel \overrightarrow{b}$, $\overrightarrow{a} \perp \overrightarrow{c}$.  
(1) Find $\overrightarrow{b}$ and $\overrightarrow{c}$.  
(2) Find the cosine of the angle $\theta$ between $2\overrightarrow{a} - \overrightarrow{b}$ and $\overrightarrow{a} + \overrightarrow{c}$.

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