
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
Madison has 15 boxes. Nine of the boxes contain pencils, five contain pens, and three boxes contain both pens and pencils. Additionally, four boxes contain markers, with two of these also having pencils but none having pens. No boxes contain all three items. How many boxes contain neither pens, pencils, nor markers?

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