
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
Select 100 numbers that satisfy the conditions:

\[ x_{1}=1, \]
\[ 0 \leq x_{1} \leq 2 x_{1}, \]
\[ 0 \leq x_{3} \leq 2 x_{2}, \]
\[ \ldots, \]
\[ 0 \leq x_{99} \leq 2 x_{98}, \]
\[ 0 \leq x_{100} \leq 2 x \]

such that the expression \( x_{1} - x_{2} + x_{3} - x_{4} + \ldots + x_{99} - x_{100} \) is maximized.

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