
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) In $\triangle ABC$, it is known that $b^{2}+c^{2}=bc+a^{2}$. The size of angle $A$ is __________.

(2) A general formula for the sequence $7,77,777,7777…$ is __________.

(3) When $0 < x < \frac{\pi }{2}$, the minimum value of the function $f(x)=\frac{1+\cos 2x+8\sin^{2}x}{\sin 2x}$ is __________.

(4) Regarding the statements about prisms:

① All faces of a prism are flat;

② All edges of a prism are of equal length;

③ All lateral faces of a prism are rectangles or squares;

④ The number of lateral faces of a prism equals the number of sides on its base;

⑤ The top and bottom faces of a prism are of the same shape and size.

Among these, the correct ones are __________ (Fill in the serial numbers).

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