
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
Solve the given equations geometrically, that is, by interpreting the absolute value $|a-b|$ as the distance between $a$ and $b$.
(a) $|x-5|=2$
(b) $|x+3|=1$
(c) $|3x-7|=9$
(d) $|x+2|=|x-5|$

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