
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
Observe the following equations:<br/>①$2=1\times 2$.<br/>②$2+4=2\times 3=6$.<br/>③$2+4+6=3\times 4=12$.<br/>④$2+4+6+8=4\times 5=20$.<br/>$\ldots $<br/>$(1)$According to the above pattern, write down the ⑤th equation:______；<br/>$(2)$Calculate according to this pattern:<br/>①$2+4+6+\ldots +34$；<br/>②$28+30+\ldots +50$.

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