
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 vector $$\overrightarrow {a}$$\=(2,1), $$\overrightarrow {a}\cdot \overrightarrow {b}$$\=10, and | $$\overrightarrow {a}$$+ $$\overrightarrow {b}$$|=$5 \sqrt {2}$$, find the magnitude of vector $$\overrightarrow {b}$$, denoted as | $$\overrightarrow {b}$$|.

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