
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
Given that $0 \le x_4 \le x_3 \le x_2 \le x_1 \le 1$ and $(1-x_1)^2 + (x_1-x_2)^2 + (x_2-x_3)^2 + (x_3-x_4)^2 + x_4^2 = \frac{9}{16}$, find $x_1$.

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