
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
A metallic weight has a mass of 20 kg and is an alloy of four metals. The first metal in this alloy is one and a half times the amount of the second metal. The mass of the second metal relates to the mass of the third metal as $3:4$, and the mass of the third metal to the mass of the fourth metal as $5:6$. Determine the mass of the fourth metal. Give your answer in kilograms, rounding to the nearest hundredth if necessary.

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