
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 $M: (x-a)^2 + (y-2)^2 = 4$ and a line $l: x-y+3=0$. When the chord intercepted by line $l$ on circle $M$ has a length of 4, find the value of $a$.

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