
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 $\overrightarrow{a}=(1,0)$, $\overrightarrow{b}=(1,1)$, $\overrightarrow{c}=(-1,1)$.
(I) For what value of $λ$ is $\overrightarrow{a}+λ \overrightarrow{b}$ perpendicular to $\overrightarrow{a}$?
(II) If $(m \overrightarrow{a}+n \overrightarrow{b}) \parallel \overrightarrow{c}$, find the value of $\frac {m}{n}$.

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