
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 function $y=|x|$ and the circle $C$: $x^2+(y-a)^2=2(a-2)^2$, where $a>0$ and $a\neq 2$, find the value of $a$ for which the graph of $y=|x|$ is tangent to circle $C$.

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