
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
What is the maximum number of solutions that the equation \(\max \left\{a_{1} x+b_{1}, \ldots, a_{10} x+b_{10}\right\} = 0\) can have, if \(a_{1}, \ldots, a_{10}, b_{1}, \ldots, b_{10}\) are real numbers, with all \(a_{i} \neq 0\)?

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