
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 a certain number of chickens are placed into several cages, and if 4 chickens are placed in each cage, there will be one chicken left without a cage. If 5 chickens are placed in each cage, there will be one cage left empty. How many chickens and how many cages are there?
2. To further promote the construction of Hainan as an international tourism island, Haikou has implemented the "Interim Measures for Rewarding Travel Agencies for Developing Source Markets" since April 1, 2012. Article 8 stipulates: Travel agencies that bring in conferences with more than 200 participants, staying in the city's Class A hotels, will be rewarded with 20,000 yuan per conference; those staying in Class B hotels will be rewarded with 10,000 yuan per conference. A travel agency brought in 18 conferences that met the criteria in May and received a total of 280,000 yuan in rewards. How many of these conferences stayed in Class A and Class B hotels, respectively?

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