
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) The constant term in the expansion of ${{(|x|+\frac{1}{|x|}-2)}^{3}}$ is _______________.

(2) In the polar coordinate system, the intersection points of the two curves ${{C}_{1}}:\rho \sin (\theta +\frac{\pi }{4})=1$ and ${{C}_{2}}:\rho =\sqrt{2}$ are $A,B$, then $|AB|=$ _______________.

(3) Given the random variable $X\sim B(2,p)$, $Y\sim N(2,{{\sigma }^{2}})$, if $P(X\geqslant 1)=0.64$, $P(0 < Y < 2)=p$, then $P(Y > 4)=$ _______________.

(4) Given the function $f(x)=2\sin x+\sin 2x$, then the minimum value of $f(x)$ is _______________.

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