
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

Denis divided a triangle into nine smaller triangles, as shown in the picture, and placed numbers in them. In the white triangles, the numbers equal the sum of the numbers in the neighboring gray triangles. After that, Lesha erased the numbers 1, 2, 3, 4, 5, and 6 and replaced them with the letters \(A, B, C, D, E\), and \(F\) in some order. The resulting arrangement of numbers and letters is shown in the picture.

Where were the original numbers placed?
(a) Instead of the letter \(A\)
(1) the number 1 was placed.
(b) Instead of the letter \(B\)
(2) the number 2 was placed.
(c) Instead of the letter \(C\)
(3) the number 3 was placed.
(d) Instead of the letter \(D\)
(4) the number 4 was placed.
(e) Instead of the letter \(E\)
(5) the number 5 was placed.
(f) Instead of the letter \(F\)
(6) the number 6 was placed.

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