
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 that $| \overrightarrow{a}|=3 \sqrt {2}$, $| \overrightarrow{b}|=4$, $\overrightarrow{m}= \overrightarrow{a}+ \overrightarrow{b}$, $\overrightarrow{n}= \overrightarrow{a}+λ \overrightarrow{b}$, $ < \overrightarrow{a}, \overrightarrow{b} > =135^{\circ}$, if $\overrightarrow{m} \perp \overrightarrow{n}$, find the value of $λ$.

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