
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 radar observation station at point A has detected a cargo ship at point B, which is $20\sqrt{2}$ nautical miles away at a bearing of 45° northeast of A. The ship is traveling at a constant speed in a straight line. After 20 minutes, the ship is observed at point C, at a bearing of 45°+θ (0°<θ<45°) east of station A, with $AC=5\sqrt{13}$ nautical miles. At point E due south of station A, it is known that $\cos \angle EAC = \frac{2\sqrt{13}}{13}$.
(1) Find $\cos\theta$.
(2) Determine the speed \(v\) of the ship (in nautical miles per hour).

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