
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
$(1)$ Find the value of $x$: $4\left(x-1\right)^{2}-16=0$;<br/>$(2)$ Calculate: $\sqrt[3]{{-64}}+\sqrt{16}×\sqrt{\frac{9}{4}}+{({-\sqrt{2}})^2}$;<br/>$(3)$ If the integer part of $9-\sqrt{13}$ is $a$ and the decimal part is $b$, find the value of $2a+b$.<br/>$(4)$ Define an operation "$\oplus $" in the real number range as follows: $a\oplus b=a^{2}-b^{2}$. Find the solution to the equation $\left(4\oplus 3\right)\oplus x=24$.<br/>$(5)$ If $\angle 1$ and $\angle 2$ are parallel, and $\angle 1$ is $36^{\circ}$ less than three times $\angle 2$, find the degree measure of $\angle 1$.

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