
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
Each participant in the school charity event brought either one encyclopedia, or three fiction books, or two reference books. A total of 150 encyclopedias were collected. After the event, two bookshelves in the library were filled, with an equal number of books on each. The first shelf contained one-fifth of all the reference books, one-seventh of all the fiction books, and all the encyclopedias. How many total participants were there in the event, and how many books did they bring?

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