
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) If the surface area of a sphere is $36\pi$, then the volume of the sphere is _______.

(2) Let the sequence $\{a_n\}$ be an arithmetic sequence with a non-zero common difference, $a_1=1$, and $a_1$, $a_3$, $a_6$ form a geometric sequence. The sum of the first 8 terms of the sequence $\{a_n\}$, $S_8$, is _______.

(3) If for $x > 0$, $y > 0$, the inequality $(x+2y)(\frac{2}{x}+\frac{1}{y}) \geqslant m$ always holds, the range of $m$ is _______.

(4) Consider the following statements: ① If a plane passes through the perpendicular of another plane, then these two planes are perpendicular to each other; ② If two lines in a plane are parallel to another plane, then these two planes are parallel to each other; ③ If one of two parallel lines is perpendicular to line $m$, then the other line is also perpendicular to line $m$. Among these, the numbers of all true statements are _______.

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