
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 vectors $\overrightarrow {a}$=(1,$m$), $\overrightarrow {b}$=(2,$n$).
(1) If $m=3$, $n=-1$, and $\overrightarrow {a}$⊥($\overrightarrow {a}$+$λ\overrightarrow {b}$), find the value of the real number $λ$;
(2) If $m=1$, and the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$ is $\frac {π}{4}$, find the value of the real number $n$.

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