
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
If $b$ is the arithmetic mean of $a$ and $c$, and $y$ is the geometric mean of $x$ and $z$, and $x$, $y$, $z$ are all positive numbers, then $(b-c)\log_{m}x+(c-a)\log_{m}y+(a-b)\log_{m}z=$ ______.

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