
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
Try to select 100 numbers such that they satisfy the following conditions:
$$
\begin{array}{c}
x_{1}=1, \quad 0 \leq x_{k} \leq 2 x_{k-1}, \quad k=2,3,\ldots, 100, \\
\text{and make } s = x_{1} - x_{2} + x_{3} - x_{4} + \cdots + x_{99} - x_{100} \text{ as large as possible.}
\end{array}
$$

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