
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
There are 200 numbers: 1, 2, 3, ..., 199, 200. Divide them arbitrarily into two groups (each with 100 numbers). Arrange one group in ascending order, denoted as $a_1 < a_2 < \ldots < a_{100}$, and the other group in descending order, denoted as $b_1 > b_2 > \ldots > b_{100}$. Try to find the value of the algebraic expression $|a_1 - b_1| + |a_2 - b_2| + \ldots + |a_{99} - b_{99}| + |a_{100} - b_{100}|$.

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