
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
An $R$ radius semicircle has a diameter $AB$ with a point $C$ determined in such a way that if $D$ is a point on the semicircle and the projection of $D$ onto $C$, then $AC + AD = l$, where $l$ is a given length. For what values of $l$ is there a solution?

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