
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
A person bought several fountain pens and ballpoint pens, with the price of a fountain pen being twice that of a ballpoint pen. When paying, it was found that the quantities of the two types of pens purchased were reversed, resulting in a 50% increase in the planned expenditure. Find the ratio of the planned purchase quantities of fountain pens to ballpoint pens.

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