
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
Solve the following equation:
$$x : \frac{3}{4} = 2 : \frac{9}{10}$$
$$\frac{0.5}{x} = \frac{0.75}{6}$$
$$x : 20 = \frac{2}{5}$$
$$\frac{3}{4}x \div 15 = \frac{2}{3}$$

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