
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 vectors $\overset{\rightharpoonup }{a }=(x, x+2)$ and $\overset{\rightharpoonup }{b }=(1, 2)$, find the value of $x$ if $\overset{\rightharpoonup }{a }$ is parallel to $\overset{\rightharpoonup }{b }$, and the value of $x$ if $(\overset{\rightharpoonup }{a }-\overset{\rightharpoonup }{b })$ is perpendicular to $\overset{\rightharpoonup }{b }$.

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