
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  $\triangle ABC$  with  $\angle A = 15^{\circ}$ , let  $M$  be midpoint of  $BC$  and let  $E$  and  $F$  be points on ray $BA$  and  $CA$  respectively such that  $BE = BM = CF$ . Let  $R_1$  be the radius of  $(MEF)$  and  $R_{2}$  be
radius of  $(AEF)$ . If  $\frac{R_1^2}{R_2^2}=a-\sqrt{b+\sqrt{c}}$  where  $a,b,c$  are integers. Find  $a^{b^{c}}$ 

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