
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 wooden Chinese chess piece "General" has the character "General" carved on one side and is smooth on the other side. When thrown from a certain height, it may land with the "General" side facing up or down. Due to the unevenness of the two sides of the chess piece, a test group conducted experiments on throwing the chess piece. The experimental data is shown in the table below:

| Number of experiments $n$ | $20$ | $40$ | $60$ | $80$ | $100$ | $120$ | $140$ | $160$ |
|---------------------------|------|------|------|------|-------|-------|-------|-------|
| Frequency of "General" side up $m$ | $a$ | $18$ | $38$ | $47$ | $52$ | $66$ | $77$ | $88$ |
| Frequency of "General" side up | $0.7$ | $0.45$ | $0.63$ | $0.59$ | $0.52$ | $0.55$ | $0.55$ | $b$ |

(1) Find the values of $a$ and $b$ in the table above.  
(2) Based on the table, estimate the probability of the "General" side facing up after it is thrown from a certain height and bounces back to the ground. (Keep two decimal places)

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