
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 planar vectors $\overrightarrow{a}=(3,4)$, $\overrightarrow{b}=(9,x)$, $\overrightarrow{c}=(4,y)$, and $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$, while $\overrightarrow{a}$ is perpendicular to $\overrightarrow{c}$.
1. Find $\overrightarrow{b}$ and $\overrightarrow{c}$.
2. If $\overrightarrow{m}=2\overrightarrow{a}-\overrightarrow{b}$ and $\overrightarrow{n}=\overrightarrow{a}+\overrightarrow{c}$, find the size of the angle between vectors $\overrightarrow{m}$ and $\overrightarrow{n}$.

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