
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
Xiaoming's family needs steel pipes to make burglar-proof windows. According to the design requirements, they need 100 pieces of steel pipes with a length of 0.8m and 32 pieces with a length of 2.5m, all of the same thickness. These materials cannot be welded together. The steel pipes of this specification available in the market are 6m long each.
(1) What are some of the cutting methods for a 6m long steel pipe? Please fill in the blanks (the leftovers are wasted):
Method ①: When only cutting 0.8m sections, the maximum number that can be cut is ___;
Method ②: After cutting one 2.5m section, the remaining part can be cut into a maximum number of 0.8m sections, which is ___;
Method ③: After cutting two 2.5m sections, the remaining part can be cut into a maximum number of 0.8m sections, which is ___.
(2) How many 6m steel pipes need to be cut using methods ② and ③ to obtain the exact required amount of each size?
(3) Investigate: Apart from the scheme in (2), which other two combined methods from (1) would require the same number of 6m steel pipes as in (2)?

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