
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
1. For what x do we have \( x < 0 \) and \( x < \frac{1}{4x} \)?
2. What is the greatest integer \( n \) such that \( 4n + 13 < 0 \) and \( n(n+3) > 16 \)?
3. Give an example of a rational number between \( \frac{11}{24} \) and \( \frac{6}{13} \).
4. Express 100000 as a product of two integers which are not divisible by 10.
5. Find \( \frac{1}{\log_2 36} + \frac{1}{\log_3 36} \).

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