
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
Consider the set  $\mathcal{T}$  of all triangles whose sides are distinct prime numbers which are also in arithmetic progression. Let  $\triangle \in \mathcal{T}$  be the triangle with least perimeter. If  $a^{\circ}$  is the largest angle of  $\triangle$  and  $L$  is its perimeter, determine the value of  $\frac{a}{L}$ .

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