
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
Suppose  $50x$  is divisible by 100 and  $kx$  is not divisible by 100 for all  $k=1,2,\cdots, 49$  Find number of solutions for  $x$  when  $x$  takes values  $1,2,\cdots 100$ .
[list=1]
[*] 20
[*] 25
[*] 15
[*] 50
[/list]

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