
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 \( a_{1}, a_{2}, \cdots, a_{50}, b_{1}, b_{2}, \cdots, b_{50} \) be distinct numbers. Consider the following equation:
\[
\left|x - a_{1}\right| + \cdots + \left|x - a_{50}\right| = \left|x - b_{1}\right| + \cdots + \left|x - b_{50}\right|
\]
This equation has a finite number of roots. What is the maximum possible number of roots?

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