
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 $g(x)$ be a polynomial of degree 300 with real coefficients, and let its roots be $s_1, s_2, \dots, s_{300}$. There are exactly 150 distinct values among
\[ |s_1|, |s_2|, \dots, |s_{300}|. \]
What is the minimum number of real roots that $g(x)$ can have?

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