
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(2, 3), B(5, 4), C(10, 8), if $\overrightarrow {AP} = \overrightarrow {AB} + \lambda \overrightarrow {AC}$ ($\lambda \in \mathbb{R}$), find the value of $\lambda$ when:  
(1) Point P is on the line $y = x$?  
(2) Point P is in the second quadrant?

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