
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
Eliška placed cakes into boxes and then built a pyramid from these boxes, as shown in the picture. Each box in a higher row contained as many cakes as the sum of cakes in the two adjacent boxes in the row below. In the three boxes marked with stars, there were three, five, and six cakes respectively.

Eliška noticed that if the marked boxes were interchanged in any way (and the cake counts in other boxes adjusted according to the previous rule), the total number of cakes would not be smaller.

How many cakes were in the marked box in the second row from the bottom?

(L. Hozová)

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