
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 a triangle $ABC$ with its three interior angles $A$, $B$, and $C$, and $A \neq \frac{\pi}{2}$.

(Ⅰ) Simplify $\frac{\sin(\frac{3\pi}{2} + A) \cdot \cos(\frac{\pi}{2} - A)}{\cos(B + C) \cdot \tan(\pi + A)}$;

(Ⅱ) If angle $A$ satisfies $\sin A + \cos A = \frac{1}{5}$,

(i) Determine whether $\triangle ABC$ is an acute triangle or an obtuse triangle, and explain the reason;

(ii) Find the value of $\tan A$.

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