
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 $\overrightarrow{m}=(1,1)$, vector $\overrightarrow{n}$ forms an angle of $\frac{3\pi}{4}$ with vector $\overrightarrow{m}$, and $\overrightarrow{m}\cdot\overrightarrow{n}=-1$.
(1) Find vector $\overrightarrow{n}$;
(2) If vector $\overrightarrow{n}$ is perpendicular to vector $\overrightarrow{q}=(1,0)$, and vector $\overrightarrow{p}=(2\sin A,4\cos ^{2} \frac{A}{2})$, find the value of $|2\overrightarrow{n}+\overrightarrow{p}|$.

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