
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 value of   $$ \sum_{1\le a<b<c} \frac{1}{2^a3^b5^c} $$   (i.e. the sum of  $\frac{1}{2^a3^b5^c}$  over all triples of positive integers  $(a, b, c)$  satisfying  $a<b<c$ )

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