
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
There is a pile of 50 candies. Xiaoming and Xiaoliang play a game. Every time Xiaoming wins, he takes 5 candies, eats 4 of them, and puts the remaining 1 candy in his pocket. Every time Xiaoliang wins, he also takes 5 candies, eats 3 of them, and puts the remaining 2 candies in his pocket. When the game ends, all the candies are taken, and the number of candies in Xiaoliang's pocket is exactly three times the number of candies in Xiaoming's pocket. How many candies did they eat in total?

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