
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 that $\sin\left(x+\frac{\pi}{2}\right)=\frac{3}{5}$, and $x$ is in the interval $(0, \frac{\pi}{2})$.
(1) Find the value of $\tan x$;
(2) Find the value of $\frac{1+2\sin x \cos x}{\sin^2 x - \cos^2 x}$.

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