
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
 $M$  is an arbitrary point inside  $\triangle ABC$ .  $AM$  intersects the circumcircle of the triangle again at  $A_1$ . Find the points  $M$  that minimise  $\frac{MB\cdot MC}{MA_1}$ .

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