
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
Determine how many integers \( x \) satisfy the inequality:
\[
\log_{10}(x-30) + \log_{10}(90-x) < 1
\]
A) 0  
B) 1  
C) 2  
D) 3  
E) Infinitely many

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