
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
Find the standard equation of the hyperbola based on the following conditions:  
\\((1)\\) It passes through points \\(P(3, \dfrac {15}{4})\\) and \\(Q(- \dfrac {16}{3},5)\\);  
\\((2)\\) The distance between the foci is \\(c= \sqrt {6}\\), it passes through point \\((-5,2)\\), and the foci are on the \\(x\\)-axis.

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