
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
Five points  $A_1,A_2,A_3,A_4,A_5$  lie on a plane in such a way that no three among them lie on a same straight line. Determine the maximum possible value that the minimum value for the angles  $\angle A_iA_jA_k$  can take where  $i, j, k$  are distinct integers between  $1$  and  $5$ .

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