
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
Jancsi and Feri each took 5 shots at a shooting target with 12 rings. On the target, there are 1 hit in the 5th, 8th, 11th, and 12th rings, and 2 hits in the 7th, 9th, and 10th rings. During the shooting, we heard that each of them had one hit in the 10th ring. We also learned that with his last four shots, Jancsi scored 7 times as many points as with his first shot; Feri scored 5 times as many points with his first four shots as with his last shot, and with his last two shots, he scored as many points as with his first two shots. - Whose hit was in the 12th ring? What could be the two boys' scores, and the sequence of Feri's hits?

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