
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 the point M(1, m) and the circle C: $x^2+y^2=4$.
(1) If there is only one tangent line to circle C passing through point M, find the value of m and the equation of the tangent line;
(2) If a line passing through point M and having equal intercepts on both coordinate axes cuts a chord of length $2\sqrt{3}$ from circle C, find the value of m.

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