
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
Compute
\[\sum_{1 \le a < b < c} \frac{1}{2^a 4^b 6^c}.\]
(The sum is taken over all triples $(a, b, c)$ of positive integers such that $1 \le a < b < c.$)

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