
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
Mr. Hu originally has 100 red cards and 100 blue cards. He can exchange 2 red cards for 1 blue card and 1 purple card, or exchange 3 blue cards for 1 red card and 1 purple card. After several exchanges, what is the maximum number of purple cards Mr. Hu can have?

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