
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
Suppose \( x_{1}, x_{2}, \ldots, x_{49} \) are real numbers such that

\[ x_{1}^{2} + 2 x_{2}^{2} + \cdots + 49 x_{49}^{2} = 1. \]

Find the maximum value of \( x_{1} + 2 x_{2} + \cdots + 49 x_{49} \).

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