
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 vectors $\overrightarrow{a}=(1, 2)$, $\overrightarrow{b}=(x, 1)$, let $\overrightarrow{u}= \overrightarrow{a}+ \overrightarrow{b}$ and $\overrightarrow{v}= \overrightarrow{a}- \overrightarrow{b}$,
(Ⅰ) If $\overrightarrow{u}\parallel \overrightarrow{v}$, find the value of the real number $x$;
(Ⅱ) If $\overrightarrow{u}\perp \overrightarrow{v}$, find the value of the real number $x$.

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