
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 are black and white pieces in a bag. The number of black pieces is twice the number of white pieces. Each time, 3 black pieces and 2 white pieces are taken out of the bag at the same time. After a certain round, 1 white piece and 31 black pieces are left. How many black pieces were there originally in the bag?

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