
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
Humpty buys a box of 15 eggs, with 3 rows and 5 columns. Each meal he removes one egg to cook and eat. If necessary, he moves one or more eggs in the box so that between meals there are always two lines of reflective symmetry. What is the smallest total number of extra egg moves he can make while he empties the box?

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