
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
In the Cartesian coordinate system, the terminal side of angle $\alpha$ passes through point $P(-3,4)$.
(1) Find the values of $\sin \alpha$ and $\cos \alpha$;
(2) Find the value of $\tan (\alpha + \frac{\pi}{4})$;
(3) Find the value of $\sin^2 (\alpha + \frac{\pi}{4}) + \sin (\alpha + \frac{\pi}{4}) \cdot \cos (\alpha + \frac{\pi}{4})$.

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