
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 circle $C$ tangent to the $x$-axis, with its center $C$ on the ray $3x-y=0 (x > 0)$, and the chord intercepted by the line $x-y=0$ on circle $C$ has a length of $2\sqrt{7}$.

 (Ⅰ) Find the standard equation of circle $C$;

 (Ⅱ) If point $Q$ is on the line $l_{1}: x+y+1=0$, and a line $l_{2}$ passing through point $Q$ is tangent to circle $C$ at point $P$, find the minimum value of $|QP|$.

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