
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 non-empty subsets $A$, $B$, $C$ of $M$. If $\forall x\in A$, $y\in B$, $z\in C$, $x < y < z$ always holds, then we call "$A-B-C$" a "sub-subset chain" of set $M$. How many "sub-subset chains" does set $M$ have?

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