
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
Find the smallest constant  $C > 0$  for which the following statement holds: among any five positive real numbers  $a_1,a_2,a_3,a_4,a_5$  (not necessarily distinct), one can always choose distinct subscripts  $i,j,k,l$  such that
\[ \left| \frac{a_i}{a_j} - \frac {a_k}{a_l} \right| \le C. \]

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