
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
Let the equation of the hyperbola C be $\frac{{x}^{2}}{{a}^{2}}$-$\frac{{y}^{2}}{{b}^{2}}$=1 (a>0, b>0), and the line passing through the focus of the parabola $y^2=4x$ and the point (0, b) is denoted as l. If one asymptote of C is parallel to l and the other asymptote is perpendicular to l, then find the equation of the hyperbola C.

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