
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
Fifteen stones are arranged in a straight line and are counted from left to right starting with $1, 2, 3, \ldots, 15$, and then from right to left such that the stone previously counted as 14 is now counted as 16, continuing to the left until the stone previously counted as 1 is now counted as 29. The pattern then reverses so that the stone that was previously counted as 2 is now counted as 30, etc. The counting continues in this pattern. Which original stone is counted as 123? Express your answer as the original stone number.

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