
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 set $\{a,b,c,d\}=\{1,2,3,4\}$, and among the following four statements:  
1. $a=1$;
2. $b\neq 1$;
3. $c=2$;
4. $d\neq 4$;  
exactly one is true.  
Find one ordered tuple $(a,b,c,d)$ that satisfies the above conditions. __________, and the total number of such ordered tuples $(a,b,c,d)$ is __________.

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