
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
Let $\overrightarrow {e_{1}}$ and $\overrightarrow {e_{2}}$ be two mutually perpendicular unit vectors. Given that $\overrightarrow {AB}=3 \overrightarrow {e_{1}}+2 \overrightarrow {e_{2}}$, $\overrightarrow {CB}= \overrightarrow {e_{1}}-\lambda \overrightarrow {e_{2}}$, $\overrightarrow {CD}=-2 \overrightarrow {e_{1}}+ \overrightarrow {e_{2}}$,

(1) If points A, B, and D are collinear, find the value of the real number $\lambda$.

(2) If points A, B, and D form a right-angled triangle, find the value of the real number $\lambda$.

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