
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 vector $\overrightarrow{m} = (1, 1)$, vector $\overrightarrow{n}$ forms an angle of $\frac{3\pi}{4}$ with vector $\overrightarrow{m}$, and $\overrightarrow{m} \cdot \overrightarrow{n} = -1$.
(1) Find the vector $\overrightarrow{n}$;
(2) Let vector $\overrightarrow{a} = (1, 0)$, vector $\overrightarrow{b} = (\cos x, \sin x)$, where $x \in \mathbb{R}$. If $\overrightarrow{n} \cdot \overrightarrow{a} = 0$, try to find the range of values for $|\overrightarrow{n} + \overrightarrow{b}|$.

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