
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
(1) Calculate $\dfrac {(1+i)^{2}}{1+2i}+ \dfrac {(1-i)^{2}}{2-i}$;
(2) If real numbers $x$ and $y$ satisfy $\dfrac {x}{1+i}+ \dfrac {y}{1+2i}= \dfrac {10}{1+3i}$, find the values of $x$ and $y$.

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