
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
Let $y_1, y_2, \ldots, y_n$ be real numbers which satisfy $|y_i| < 1$ for $i = 1, 2, \dots, n,$ and \[|y_1| + |y_2| + \dots + |y_n| = 15 + |y_1 + y_2 + \dots + y_n|.\] What is the smallest possible value of $n$?

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