
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
In a magical land, twelve stones are arranged in a straight line from left to right and labeled sequentially as $1, 2, 3, \ldots, 12$. The wizard starts counting these stones in a pattern; first from left to right, then continues again from right to left without including the first and the last. The pattern is repeated, but each time the wizard skips counting the two stones at either end of the sequence not yet skipped. Identify the original stone numbered when the count reaches $150$.

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