Your task is to, as an astrophysicist, rewrite to improve the proposal based on the reviewers' comments. You need to only reply the new version of proposal.

Reviewer comments: 「Strengths: Scientifically well motivated, a very careful pre-selected targets, and a good-designed project. Weaknesses: There are basically a couple of key issues that are not addressed in the science justification. First, radio sources in the VLASS catalog can be variables except AGN or Galactic stars, e.g., supernovae, tidal disruption events, long gamma-ray bursts, etc. The proposers exclude the possibilities of the selected sources to be AGN, but there is not specific information provided here about these radio sources. Are the sources really similar with the PRSes of FRB 20121102A and 20190520B in term of radio spectra, e.g., spectral index, variability? Otherwise, they can still possibly originate from the other transients. Much more rigorous evaluation of the selection criteria, that actually install some quantitative confidence of the likelihood that the selected sources match the definition of PRSs as defined in e.g. the Law et al. paper cited in the proposal, would improve the proposal. Second, the PRS-FRB association is not well established currently. Just as the proposers mentioned, it’s not conclusive that repeating FRBs have to be associated with PRSes. To date, there have been 8 repeaters localized to exact positions in their host galaxies, while only 3 repeaters are confirmed with PRS associations. Moreover, none of 12 localized apparent non-repeaters turn out to be associated with PRSes. Even though the PRS-FRB association does exist, there is much less than 50% chance to detect FRBs. Third, the sciences of non-detection case are unspecific. Even if we assume most of the selected sources are truly repeaters, it’s still very likely to miss detection considering many factors, such as, beaming angle of coherent emission, free-free absorption by ambient medium, emission band-limited for FAST, etc. In general, high-cadence observations are merely recommended once the sources have been confirmed to repeat. If there is no any clue of repetition, it’s non-sense to talk about active episode or non-Poissonian process. In fact, non-detection can neither establish nor rule out anything, the PRS-FRB association is still an open question. It is unclear how many FRBs the proposers expect to detect from their sample given the diversity in the 'on' and 'off' cycles of the FRBs with long-term periodicities. Technically, the authors may need to focus on a more selected targets, as the positions are accurate enough, no need for recording data for 19 beams.」

Proposal: ```Hundreds of fast radio bursts (FRBs) have been detected over the past decade , most of which are one-off FRBs, and only 22 were found to be repeating FRBs.
With the development of instrumentation and algorithms, dozens of FRBs have been located in galaxies , including both repeating and non-repeating FRBs.
Studies of the host galaxies and environments of accurately localized FRBs offer an excellent opportunity to discern FRB progenitors.

The first localized repeating FRB source, FRB~20121102A , and its newly discovered analog FRB~20190520B  are located in star-forming regions of dwarf galaxies with persistent radio sources (PRS).
It is worth noting that both PRSes are clearly offset from the host galaxies' center.
Both FRBs have large rotation measures (RM), which vary dramatically on the time scale of months , indicating that the two FRBs are in highly magnetised environments, likely associated with their PRSes.
Recently, we also found that the degree of polarization of several repeating FRBs evolves with frequency , which confirms the complex environment near repeating FRBs.

There is yet no conclusive evidence for repeating FRBs to be preferentially associated with PRSes due to insufficient sample size.
However, the fact that repeating FRBs are in complex environments and only repeating FRBs are found to be associated with PRSes raises the possibility of searching for repeating FRBs toward PRSes, particularly those misidentified as active galactic nuclei (AGN) .
FAST has unparalleled sensitivity which means that FAST can detect bursts that other telescopes cannot.
During one active period of the same repeating FRB, FAST can detect hundreds of times more bursts than other telescopes, such as FRB~20121102A and FRB~20201124A, greatly expanding the detection energy range of repeating FRBs.
Hence, we propose to use FAST to search for FRBs in nearby galaxies with PRSes.

PRSes are as luminous as AGN, which is the most common class of extragalactic radio source .
Given the similar densities of PRSes and AGN in dwarf galaxies , it is likely that PRSes have already been detected and perhaps misidentified as AGN .
Our analysis of the burst rate energy distribution of FRB 20121102A shows a characteristic peak below which the rate drops , deviating from a single power law.
The existence of a characteristic peak energy in the burst rate-energy distribution would favor nearby sources for a targeted FRB search, assuming any survey has to conform to the same all sky FRB event rate.

Through cross-matching the VLASS catalog , AllWISE catalog , and SDSS DR16 spectroscopic catalog , we selected sources according to the following
1) excluding sources that are stars or likely to be AGN (labeled as AGN in SDSS or by \textit{WISE} color selection); 2) radio position significantly offset from the peak in optical brightness; 3) redshift $\le0.05$;
4) a projected distance greater than 1~kpc between the optical and radio detections.
This produced 87 unique candidates.
Visual inspection to remove objects with extended radio emission, and those where the SDSS extracted source was off of the galaxy's nucleus and the radio source was on the true nucleus left 9 candidates.
The luminosities and fluxes of these candidates are typical for the pre-inspection sources, but should have no remaining AGN contamination.
The resulting sample (accessible to FAST) contains 9 nearby PRS candidates as our targets.

Repeating FRBs seems to have active  and silent episodes. The active episode can last for longer than one month .
The switching time between the two states can range from a few days to several months .
During an active episode, FAST can detect a burst within about half an hour.
With half an hour of observation per source per month, an active episode of repeating FRBs will be unlikely to be missed.

Any detection would be a major discovery, expanding the small number of FRB-PRS samples and strengthening the link between FRBs and PRSes, which favors an evolutionary picture of the repeating population in that the burst rate drops while the PRS fade as discussed in our upcoming Nature paper.
Non-detection would also be publishable as it would meaningfully constrain the association between FRBs and PRSes.
We thus propose regular monitoring of a typical, but pure, sample of nearby PRS candidates.```