
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
Positive integers \(a_{1}, a_{2}, \cdots, a_{18}\) satisfy the following two conditions: 
1. \(a_{1} < a_{2} < a_{3} < \cdots < a_{18}\)
2. \(a_{1} + a_{2} + \cdots + a_{18} = 2001\)

What is the maximum value of \(a_{9}\)?

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