
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
(1) Given that $a < 0$, the terminal side of angle $\alpha$ passes through point $P(-3a, 4a)$. Find the value of $\sin\alpha + 2\cos\alpha$.
(2) Given that $\tan\beta = 2$, find the value of $\sin^2\beta + 2\sin\beta\cos\beta$.

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