
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
Find the length of the hypotenuse AC in a right triangle ABC, where AC is the hypotenuse, and segments AD and AE are drawn from vertex A to points D and E on the hypotenuse AC, such that AD = sin(x) and AE = sin(x + π/3), and points D and E divide the hypotenuse AC into three segments such that CD : DE : EA = 1:1:2.

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