
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
Suppose the original proposition is "If $a < b$, then $a + c < b + c$." where $a, b, c \in \mathbb{R}$.

(1) Write its converse, inverse, and contrapositive propositions;  
(2) Determine the truth of these four propositions;  
(3) Write the negation of the original proposition.

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