
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 hyperbola (C) in the Cartesian coordinate plane $(xOy)$, its center is at the origin, and its foci are on the $x$-axis. $F\_1$ and $F\_2$ are the left and right foci respectively, with $F\_1(-5,0)$, and the eccentricity is 5.
(I) Find the standard equation of the hyperbola (C);
(II) A point P on the right branch of the hyperbola satisfies $|PF_{1}|+|PF_{2}|=14$. Determine the shape of $\triangle PF\_1F\_2$.

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