
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
Five numbers, 3, 6, 9, 12, and 15, are to be placed in a cross-shaped grid with one square at the center and four surrounding it. The numbers should be arranged such that the sum of the three numbers in the horizontal row equals the sum of the three numbers in the vertical column, and the number 15 must be placed in the center square. What is the largest possible value for these sums?
[asy] draw((0,0)--(3,0)--(3,1)--(0,1)--cycle); draw((1,-1)--(2,-1)--(2,2)--(1,2)--cycle); [/asy]
A) 27
B) 30
C) 33
D) 36
E) 39

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