
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
An artificial lake, with a volume of $9900 \mathrm{~m}^{3}$, can be filled with water through two sluice gates. If the first sluice gate is open for 10 hours and the second for 14 hours, the lake fills up; it also fills up if the first sluice gate operates for 18 hours and the second for 12 hours. For how long must both sluice gates be open equally to fill the lake?

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