Repeated measures ANOVA - appropriate test?

Hi - I'm working on data from a psychophiscs experiment. Briefly I have 10 participants, 3 conditions, and >100 trials for each participant-condition combination. I want to see if reaction time is different between the three conditions.

From the literature, I think a repeated measures ANOVA is the right way to do this. But I'm confused. Are the trials the "repeated measures" in this case? In most examples, the repeated measure is usually equal between participants. In my data the number of trials differs between participants. Can a RM-ANOVA handle data like this?

Thanks a lot.
Thanks a lot for replying. I have two dependent variables I'd like to test: horizontal pointing error and reaction time. Both are continuous and (approximately) normal.
Just following up on my original question. I'm unclear how to set up a repeated measures anova when the data is different length between participants. In brief I have data organized like this: y_i, x1_i, x2_i.

y_i is continuous and normally distributed.
x1_i is the participant label, 10 in total.
x2_i is the condition label, 3 levels.
i is trial number, ~3000 total. ~100 trials per condition-participant, although this differs.

I want to know whether mean y differs between the conditions x2. I'd usually run a 1-way independent-sample anova grouping with x2, however from what I read a repeated measures anova is more appropriate. Is this right? If so, can a repeated measures anova use data with different numbers of trials for the condition-participant combinations?

Thanks a lot. I'm just beginning, so sorry if anything unclear!