
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
(1) True or false questions (determine the truth value of statements and explain the reason):
1. If $a > b$ and $c = d$, then $ac > bd$.
2. If $\frac{a}{c^{2}} < \frac{b}{c^{2}}$, then $a < b$.
3. If $a > b$ and $c > d$, then $a - c > b - d$.
4. If $\frac{c}{a} > \frac{d}{b}$, then $bc > ad$.

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