
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
To understand the growth situation of the fish in the fish farm, the fish farmer caught 20 fish from the pond and weighed them as follows:

| Mass (kg) | 1.0 | 1.2 | 1.5 | 1.8 |
|-----------|-----|-----|-----|-----|
| Frequency | 4   | 5   | 8   | 3   |

$(1)$ Please directly write down the median of the sample;<br/>$(2)$ Please calculate the sample mean, and estimate the average mass of this type of fish in the pond;<br/>$(3)$ If the fish farmer marks each fish caught and then releases them back into the pond, after some time (neglecting any changes in the fish's mass during this time), 100 fish are caught from which 2 are marked. Please estimate the total mass of the fish in the pond.

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