
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 maximal number of solutions can the equation have   $$ \max  \{a_1x+b_1, a_2x+b_2, \ldots, a_{10}x+b_{10}\}=0 $$  where  $a_1,b_1, a_2, b_2, \ldots , a_{10},b_{10}$  are real numbers, all  $a_i$  not equal to  $0$ .

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