
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
The set $A = \{a, b, c, d, e\}$ has 5 elements, and the set $B = \{m, n, f, h\}$ has 4 elements. Then  
(1) The number of different mappings that can be established from set $A$ to set $B$ is \_\_\_\_\_\_\_\_.  
(2) The number of different mappings that can be established from set $B$ to set $A$ is \_\_\_\_\_\_\_\_.

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