
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
Luke has 28 pieces of banana gum and 36 pieces of apple gum. Some of the pieces are in complete packs, while others are loose. Each complete pack contains exactly $y$ pieces of gum. If Luke loses two packs of banana gum, then the ratio of the number of pieces of banana gum he has to the number of pieces of apple gum will be the same as if he instead finds 3 packs of apple gum. Find $y$.

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