
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
A convex  $ABCDE$  is inscribed in a unit circle,  $AE$  being its diameter. If  $AB = a$ ,  $BC = b$ ,  $CD = c$ ,  $DE = d$  and  $ab = cd =\frac{1}{4}$ , compute  $AC + CE$  in terms of  $a, b, c, d.$ 

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