
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 the sum:
\[ \sum_{1\leq a < b \leq c} \frac{1}{3^a 2^b 7^c}. \]
(The sum is taken over all triples \( (a, b, c) \) of positive integers such that \( 1 \leq a < b \leq c \).)

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