
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 right triangle $ABC$, it is known that $AC=4, BC=1$. $P$ is a moving point on the hypotenuse $AB$ (excluding endpoints), and the distances from $P$ to the two legs are denoted as $d_1$ and $d_2$, respectively. Calculate the minimum value of $\left(\frac{1}{d_1}+\frac{1}{d_2}\right)$.

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