
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
The Chinese sexagenary cycle is a method of recording years using a combination of 10 Heavenly Stems (namely, Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui) and 12 Earthly Branches (namely, Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai). The pairing method involves writing the Heavenly Stems in a row in sequence (repeating every 10), and then writing the Earthly Branches in sequence below them (repeating every 12), as shown below:  
Jia Yi Bing Ding Wu Ji Geng Xin Ren Gui Jia Yi Bing Ding Wu…  
Zi Chou Yin Mao Chen Si Wu Wei Shen You Xu Hai Zi Chou Yin…  
Each column represents a year, for example, the year 2002 is the year of Ren Wu.  
(1) What is the next Ren Wu year?  
(2) The Jiawu War and the Wuxu Reform happened at the end of the 19th century, in which years did they occur?  
(3) Which years in the 20th century are Geng Shen years?

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