
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 real constant \( C \) such that for any positive real numbers \( a_{1}, a_{2}, a_{3}, a_{4} \) and \( a_{5} \) (not necessarily distinct), one can always choose distinct subscripts \( i, j, k \) and \( l \) such that
$$
\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{i}}\right| \leqslant C.
$$

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