
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 points A(1, -2), B(2, 1), C(3, 2), and D(2, 3).
(1) Calculate $\overrightarrow{AD} + \overrightarrow{BD} - \overrightarrow{BC}$;
(2) If $\overrightarrow{AC} + \lambda \overrightarrow{AB}$ is perpendicular to $\overrightarrow{CD}$, find the value of $\lambda$.

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