
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 triangle $ABC$, an inscribed circle touches the sides $AB, AC, BC$ at points $C_1, B_1, A_1$ respectively. Find the radius of the excircle $w$, which touches the side $AB$ at point $D$, the extension of side $BC$ at point $E$, and the extension of side $AC$ at point $G$. It is known that $CE = 6$, the radius of the inscribed circle is $1$, and $CB_1 = 1$.

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