
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 two circles \\({{C}\_{1}}:{{(x+3)}^{2}}+{{(y-1)}^{2}}=4\\) and \\({{C}\_{2}}:{{(x-3)}^{2}}+{{(y-4)}^{2}}=1\\). A line \\(l\\) passes through point \\(A(-2,3)\\) and the chord it cuts on circle \\({{C}\_{1}}\\) has a length of \\(2\sqrt{3}\\).

\\((\\)Ⅰ\\()\\) Find the equation of line \\(l\\);

\\((\\)Ⅱ\\()\\) Investigate whether there exists a point \\(P\\) on line \\(l\\) such that the lengths of the tangents from \\(P\\) to circle \\({{C}\_{1}}\\) (\\(PM\\)) and to circle \\({{C}\_{2}}\\) (\\(PN\\)) are equal. If such point \\(P\\) exists, find the coordinates of all such points \\(P\\).

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