
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
If the digits \( a_{i} (i=1,2, \cdots, 9) \) satisfy
$$
a_{9} < a_{8} < \cdots < a_{5} \text{ and } a_{5} > a_{4} > \cdots > a_{1} \text{, }
$$

then the nine-digit positive integer \(\bar{a}_{9} a_{8} \cdots a_{1}\) is called a “nine-digit peak number”, for example, 134698752. How many nine-digit peak numbers are there?

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