
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
The daily records of the material entering and leaving a certain warehouse are shown in the table below (positive numbers represent incoming material, negative numbers represent outgoing material):

| Quantity (tons) | $-3$ | $4$ | $-1$ | $2$ | $-5$ |
|-----------------|-----|----|-----|----|-----|
| Number of times | $2$ | $1$ | $3$ | $3$ | $2$ |

$(1)$ Did the material in the warehouse increase or decrease compared to the original amount? Please explain your reasoning.  
$(2)$ Based on the actual situation, there are two options:  
Option 1: The cost of transporting each ton of material is $5$ yuan for incoming and $8$ yuan for outgoing.  
Option 2: The cost of transporting each ton of material, whether incoming or outgoing, is $6$ yuan. From the perspective of saving transportation costs, please explain which option is more appropriate.

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