
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
Points $P$ and $Q$ are 12 units apart, points $Q$ and $R$ are 7 units apart, and points $R$ and $S$ are 5 units apart. If $P$ and $S$ are as close as possible, find the distance between them.

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