
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
Calculate  
 $$\frac {567+345\times 566}{567\times 345+222}$$  
 $$\frac {1\times 2\times 3+2\times 4\times 6+\ldots+100\times 200\times 300}{2\times 3\times 4+4\times 6\times 8+\ldots+200\times 300\times 400}$$．

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