The questions states that the aircraft can not 'contact an Air Traffic Service provider'. It does not state that there is a radio failure.

The general guidance if the aircraft has to depart its assigned track / level and can not contact ATC:

1. Broadcast warnings on the VHF frequency in use or the emergency frequency or use the transponder to squawk 7500 / 7700 or use CPDLC etc. The question asks for the 'initial action' and so this is the answer.

2. Follow the procedures in Doc 7030

3. Split levels to regain some separation. For example climb or descend by 500 ft if normal separation is 1000 ft.

More details from: ICAO ANNEX 2 - Attachment B. Unlawful Interference

General

The following procedures are intended as guidance for use by aircraft when unlawful interference occurs and the aircraft is unable to notify an ATS unit of this fact.

Procedures

If the pilot-in-command cannot proceed to an aerodrome in accordance with the rules in chapter 3, 3.7.2., he/she should attempt to continue flying on the assigned track and at the assigned cruising level at least until able to notify an ATS unit or until within radar or ADS-B coverage.

When an aircraft subjected to an act of unlawful interference must depart from its assigned track or its assigned cruising level without being able to make radiotelephony contact with ATS, the pilot-in-command should, whenever possible:

a) Attempt to broadcast warnings on the VHF emergency frequency and other appropriate frequencies, unless considerations aboard the aircraft dictate otherwise. Other equipment such as on-board transponders, data links, etc., should also be used when it is advantageous to do so and circumstances permit; and

b) Proceed in accordance with applicable special procedures for in-flight contigencies, where such procedures have been established and promulgated in Doc 7030 - Regional Supplementary Procedures; or

c) If no applicable regional procedures have been established, proceed at a level which differs from the cruising levels normally used for IFR flight in the area by 300 m (1000 ft) if above FL290 or by 150 m (500 ft) if below FL290.