
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
Joanna collects marbles that are either blue, red, green, or purple. Half of her marbles are blue, one fifth are red, seven are green, and she has at least one purple marble. Find the smallest number of purple marbles Joanna could have.

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