Start from what the smear actually proves. A PAP report of CIN III / HSIL is a flag from a screening test, not a final diagnosis. The lesion could be purely intraepithelial or could already harbour early invasion, and a smear cannot distinguish these. So the management chain is: abnormal smear, then a diagnostic confirmation, then treatment.
The confirmation step in cervical disease is always colposcopy. Under magnification the clinician applies acetic acid and Lugol iodine, identifies the worst area, and obtains tissue. For a high grade lesion the most efficient way to do this is an excisional biopsy that also functions as treatment, which is LEEP. The loop cuts out the transformation zone and yields an intact specimen that the pathologist can examine for any invasive focus.
Why not the others? Removing the whole uterus for a lesion that has not invaded is over-treatment and discards the very tissue you need to read. Cryotherapy freezes the surface and destroys it without producing a specimen, which is unacceptable when you must exclude invasion in HSIL. Cold knife conization is the answer only in special situations such as a lesion running up the endocervical canal, an unsatisfactory colposcopy, or suspected microinvasion, so it is not the default next move.
Hence the immediate, single best step that both diagnoses and treats is colposcopic evaluation followed by LEEP.
\[\boxed{\text{Colposcopy and LEEP}}\]