
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 $\overrightarrow {a}$ and $\overrightarrow {b}$ satisfy $|\overrightarrow {a}|=\sqrt {3}$, $|\overrightarrow {b}|=2$, and $\left(2\overrightarrow {a}-3\overrightarrow {b}\right)\bot \left(2\overrightarrow {a}+\overrightarrow {b}\right)$.

(1) Find the angle $\theta$ between vectors $\overrightarrow {a}$ and $\overrightarrow {b}$.

(2) If $|\overrightarrow {a}+\lambda \overrightarrow {b}|=3$, find the value of the real number $\lambda$.

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