
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 in $\triangle ABC$, the sides opposite to the angles $A$, $B$, and $C$ are respectively $a$, $b$, and $c$, and $\cos A= \frac {2 \sqrt {5}}{5}$, $\cos B= \frac {3 \sqrt {10}}{10}$.  
(Ⅰ) Find the value of $\cos (A+B)$;  
(Ⅱ) If $a= \sqrt {10}$, find the area of $\triangle ABC$.

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