
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
Let $A = \left\{a_1, a_2, a_3\right\}, B = \{-1, 0, 1\}$.
(1) How many distinct mappings are there from $A$ to $B$?
(2) Determine the number of mappings $f: A \rightarrow B$ that satisfy $f(a_1) > f(a_2) \geqslant f(a_3)$.

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