STUDENT PILOT ON SOLO CROSS COUNTRY GETS CONFUSED DEPARTING PSP AND TAKES OFF WITHOUT CLEARANCE FROM THE TOWER.

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AS A STUDENT PLT; I WAS COMPLETING MY 100 MI; 3-LEG FLT TO PALM SPRINGS. APCHING THE AIRSPACE I WAS ADVISED BY THE ATIS TO CONTACT SOCAL APCH PRIOR TO CONTACTING THE TWR. AFTER LNDG I WAS ADVISED BY GND TO CONTACT SOCAL DEP (ON GIVEN FREQ) AND TO TAXI TO RUN-UP AREA FOR DEP. I THEN SWITCHED THE RADIO TO MONITOR SOCAL DEP (AS I THOUGHT WAS THE REASON FOR GIVING ME THE FREQ; I REALIZE NOW IT WAS THE FREQ TO CONTACT AFTER DEPARTING; AND NOT AT THAT MOMENT). AFTER HOLDING SHORT IN THE RUN-UP AREA FOR SOME TIME; I CONTACTED SOCAL DEP AND ASKED IF I WAS CLR TO TAKE OFF ON THE ACTIVE (RWY 31R): (KEEPING IN MIND THAT I CONTACTED APCH TO LAND; PRIOR TO TWR I THOUGHT I WOULD DO THE SAME PRIOR TO DEP; FOLLOWING THE SAME SEQUENCE). DEP THEN TOLD ME TO CONTACT THE UNICOM AND LET ANY ACFT KNOW THAT I WOULD BE TAKING OFF. I ANNOUNCED ON THE UNICOM FOR ANY TFC APCHING MY ACTIVE RWY TO PLEASE ADVISE; VERY CAUTIOUSLY CHKED FOR TFC AND PROCEEDED ON MY WAY. IMMEDIATELY AIRBORNE SOCAL ADVISED OF PLTDEV AND TWR WANTED ME TO COPY THEIR NUMBER. AS A STUDENT PLT; RADIOS ARE ALWAYS INTIMIDATING AND I WAS TRYING TO DO EXACTLY WHAT I WAS TOLD; FROM GND TELLING ME TO CONTACT SOCAL DEP AND SOCAL TO ANNOUNCE ON THE UNICOM. WHEN I FELT A RED FLAG IN MY MIND; GO UP; AFTER SOCAL TOLD ME TO CONTACT UNICOM I SHOULD HAVE CALLED BACK AND QUESTIONED IF THAT WAS ENTIRELY CORRECT OR IF I SHOULD CONTACT TWR (IT DOES NOT HURT TO ASK QUESTIONS WHENEVER I MAY FEEL THE NEED). I ALSO FEEL IT WAS IMPORTANT FOR ME TO NOTE THE HIERARCHY. THAT THE TWR HAS CTL OVER THAT AIRSPACE; NOT SOCAL AND TWR WILL ALWAYS BE THE FINAL WORD FOR APCHING OR DEPARTING ACFT.