
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
A player's shooting results at the free-throw line are recorded in the table below:

| Number of Shots $n$ | $50$ | $100$ | $150$ | $200$ | $300$ | $400$ | $500$ |
|----------------------|------|-------|-------|-------|-------|-------|-------|
| Number of Makes $m$  | $28$ | $49$  | $78$  | $102$ | $153$ | $208$ | $255$ |
| Make Frequency $m/n$ | $0.56$ | $0.49$ | $0.52$ | $0.51$ | $0.51$ | $0.52$ | $0.51$ |

Based on the data above, estimate the probability that this player will make a shot at the free-throw line.

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