
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 sets $A=\{x\mid (x-2)(x+5) < 0\}$ and $B=\{x\mid x^{2}-2x-3\geqslant 0\}$, with the universal set $U=R$, determine the sets $A\cap B=$ \_\_\_\_\_\_\_\_ and $A\cup ({{\complement }_{U}}B)=$ \_\_\_\_\_\_\_\_.

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