
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
Assume there is a set $A=\{a, b, c, d\}$ and another set $B=\{1, 2, 3, 4, 5, 6\}$. How many different mappings from set $A$ to set $B$ satisfy $f(a) \leq f(b) \leq f(c) \leq f(d)$?

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