
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 the ratio $x: y: z$ if

$$
(5 x + 4 y - 6 z) : (4 x - 5 y + 7 z) : (6 x + 5 y - 4 z) = 1 : 27 : 18
$$

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