
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
Given the set $M=\{1,2,3,4,5,6\}$, and sets $A$, $B$, $C$ are non-empty subsets of $M$. If for all $x \in A$, $y \in B$, $z \in C$, the condition $x<y<z$ always holds, then "A-B-C" is called a "subset chain" of set $M$. The total number of "subset chains" of set $M$ is \_\_\_\_\_\_.

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