
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 $\overrightarrow{n}$ has an angle of $\dfrac {3π}{4}$ with vector $\overrightarrow{m}$, and $\overrightarrow{m} \cdot \overrightarrow{n}=-1$.
(1) Find vector $\overrightarrow{n}$;
(2) Let vector $\overrightarrow{a}=(1,0)$, vector $\overrightarrow{b}=(\cos x,\sin x)$, where $x \in R$, if $\overrightarrow{n} \cdot \overrightarrow{a}=0$, find the range of $| \overrightarrow{n}+ \overrightarrow{b}|$.

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