
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 $$\overrightarrow {a}=(1，2)$$ and $$\overrightarrow {b}=(-3，4)$$
(1) Find the value of $$|3 \overrightarrow {a}- \overrightarrow {b}|$$;
(2) If $$\overrightarrow {a}⊥( \overrightarrow {a}+λ \overrightarrow {b})$$, find the value of λ.

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