
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
Consider a 4x4 magic square with the following entries not written in base 10:
```
[asy]
unitsize(0.75cm);
for (int i=0; i<5; ++i) {
draw((0,i)--(4,i),linewidth(0.7));
draw((i,0)--(i,4),linewidth(0.7));
}
label("1",(1.5,3),N);
label("2",(2.5,0),N);
label("3",(0.5,1),N);
label("4",(0.5,0),N);
label("10",(1.5,2),N);
label("14",(3.5,0),N);
label("15",(2.5,3),N);
label("12",(2.5,2),N);
label("13",(3.5,3),N);
label("16",(0.5,3),N);
label("1A",(3.5,1),N);
label("20",(1.5,0),N);
label("17",(1.5,1),N);
label("18",(3.5,2),N);
label("F",(2.5,1),N);
label("2B",(0.5,2),N);
[/asy]
```
In which base will the sums of numbers in every row, column, and diagonal be equal?

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