
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
In the continued fraction

$$
P+\frac{1}{A+\frac{1}{B+\frac{1}{H+\frac{1}{0}}}}
$$

non-zero digits are substituted instead of the letters. What is the smallest possible result in this case? (As usual, different letters correspond to different digits).

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