
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
In a plane, there are three types of relationships between two lines: intersecting, parallel and coincident. Given α and β are two intersecting planes, the projections of two lines $l_1$ and $l_2$ onto plane α are lines $S_1$ and $S_2$, and their projections onto plane β are lines $t_1$ and $t_2$. Write a sufficient condition that can always determine that $l_1$ and $l_2$ are skew lines based on the positional relationship between $S_1$ and $S_2$, as well as $t_1$ and $t_2$: .

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