
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
Two circles \( C_1 \) and \( C_2 \) are given by \( C_1: x^2 + y^2 = a^2 \) and \( C_2: (x-b)^2 + (y-c)^2 = a^2 \) respectively. If they are tangent to each other, calculate the value of \( \frac{b^2+c^2}{a^2} \).

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