
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
Consider a right-angled triangle  $ABC$  with  $\angle C = 90^o$ . Suppose that the hypotenuse  $AB$  is divided into four equal parts by the points  $D,E,F$ , such that  $AD = DE = EF = FB$ . If  $CD^2 +CE^2 +CF^2 = 350$ , find the length of  $AB$ .

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