
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 \( y_1, y_2, \ldots, y_m \) be real numbers which satisfy \( |y_i| \leq \frac{1}{2} \) for \( i = 1, 2, \dots, m, \) and 
\[
|y_1| + |y_2| + \dots + |y_m| = 10 + |y_1 + y_2 + \dots + y_m|.
\]
What is the smallest possible value of \( m \)?

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